National Identification Numbers
Sweden:

Sweden
Europe
Sweden
Name: Personnummer
Format: YYMMDD±NNGC
YYMMDD- date of birth
- changes in + if person > 100 year
NN is to make number unique
G is for gender detection odd is male, even is female
C is for a control number

Introduced Jan 1st 1947

Exceptions 
Foreigners for limited time in Sweden can get a Samordningsnummer (date will be +60)
Organiations and companies have Organisationsnummer where the month will be 20 or higher.

See also http://www.skatteverket.se/download/18.b7f2d0103e5e9ecb08000127/717b03.pdf 

Norway:
Name: Birthnumber
Format: DDMMYY99999

Person number consistes of three individual digits and 2 control digits
The individual numbers are selected out of a range based on the yearperiod of birth (1854-1899 the range is 500-749, for the years 1900-1999 the range is 000-499, for the years 2000-2039 the range is 500-999.)
Males do have an odd individual number, females an even.

Exceptions
For the years 1940-1999, the range 900-999, was used for immigrants and adoptions
Iceland:
Name: Kennitala, Icelandic ID Number
Format: DDMMYY-9999

Both for persons, organisations and companies
The first 6 digits provide the date of birth (10th digit provides the century (9 for 1900-1999, 0 for 2000-2099)

Digit 7 and 8 provide a random id number given by the registration. 
Digit 9 is a control number.
Finland: 
Name: Henkilötunnus
Format: DDMMYYC999Q

where:
DDMMYY is date of birth
Followed by a century indicator (- for 19th, + for 20th, A for 21st century
followed by a 3-digit personal identification number (odd for male, even for female) 
ending with a control character (kind of mod 31 on the first 9 digits)
Ireland:

Name: Personal Public Service Number
Format: 134567A

Note that the number is not a national identifier and usage is strongly regulated by law

Excetions:
There might be an addition W after the control character indication a gender (Wife or the person with the original id - this is deprecated since 1991)
There might be other characters added in case the same person has multiple jobs at same company  
United Kingdom
Name: National Insurance number (NINO)
Format: AA 99 99 99 A
This is not an official identification number.

Each baby born in the UK also receives a National Health Service Number
Format: 999-999-9999 
The last digit will be the control digit. 

Note: Numbers often change when moving to a different part of the country and having to change General Practitioners, the ratio is more often more one person - many numbers than one person - one number. The National Programme for Information Technology (NPfIT) has also shown that one person can have many numbers.
Spain: 
Name: Documento Nacional de Identidad (DNI)
Format: 99999999-A 

Exceptions: foreigners issued with a similar identity card, with a number in the format A9999999-A where the first character can be an X or later an Y. In that case it's normally called Número de Identificación de Extranjeros (Foreigner's Identity Number).
Belgium:
Name: National Number (Rijksregisternummer / Le numéro de registre national en Belgique)
Format: YYMMDD99999

Where the first 6 digits are the day of birth, the next 3 digits are a unique serial number and the last two digits are control numbers. The 3 serial numbers are odd for males and even for females.

Exceptions: 
For foreigners there might be 20 or 40 added to the month (pending on whether the gender is known)

France:
Name:
Format: 9YYMM9[9/C/99]999999

Where:
first digit is indicating male (1) or female (2)
Followed by the year and month of birth
Followed by 2 or 3 digits or 1 digit and 1 character to indicate the department of origin, or in case of 1 digit and one character of area in metropolitan France, or 3 digits for overseas areas
Followed by a 3 digit 'COG' number, the commune of origin (2 digits for overseas origin)
Followed by a sequential number identifying people born in same year, month and place
Followed by a 2 digit control number (modulo 97)

Exceptions can be there in rare cases if place or date of birth is unknown or in case on one place and in one month there will be more people than 999!

   

Denmark:
Name:CPR-nummer or personnummer
Format: DDMMYY-SSSS

where
DDMMYY is date of birth
next 4 digits are a sequence number where the 1st digit provides the century of birth and the last digit is odd for males and even for females

The sequence numbers ought to be chosen on  modulo 11 base to control the numbers, but as the Male population born Jan 1st, 1965 outnumbered the sequence numbers the check will not work always.


Germany:

No legalized identification number available
Lithuania:

Name: Asmens kodas
Format: GYYMMDD999C

where
G is gender and century, 
YYMMDD is the birthday, 
999 is birth serial number in that day, and
C is checksum digit.

The first number shows both the person's gender, and the first two digits of the birth year - odd for males, even for females. It is calculated by taking the first two digits of the year (for example, 19 for 1982), subtracting 16, and (if the person is female) adding 1.
Latvia:

Name:Personas kods
Format: DDMMYY-99999

where 
The first represent the date of birth
the latter 5 are randomly generated.
Estonia:

Name: Isikukood (IK)
Format: 9YYMMDD9999

where:
The first digit represents the gender (odd for male and even for female) together with an century indication ( 1-2 19th century, 3-4 20th century, 5-6 21st century)
Followed by the date of birth
Followed by a 3 digit sequential number for people born on that date
Ending with a control digit 

Exceptions:
The concept of century was not clearly defined in the relevant standard during 2000, causing some people born during that year to have a 20th century prefix and others a 21st century prefix in their identification code
Italy:
Name: Codice fiscale
Format : CCCCCCYYMDD99999

where
the first 3 characters represent the first 3 consonants of the family name (X if there are not enough consonants)
Followed by 3 characters representing the 1st, 3rd and 4th consonant of the first name (X if there are not enough consonants)
Followed by the date of birth including a gender identification, the month is represented by the characters A-E, H, L, M, P, R-T (where the number of the month is represented by the letter in this list), followed by the day of birth but added by 40 for a female.
Followed by a 4-digit area code (or coutry codes for foreigners)
Ending with a parity code as control digit

Exception:
An exception algorithm exists in case of perfectly matching codes for two persons. 
Austria

In Austria there is no one official system, there are basically 2 systems:

Name: Social Security Number (SSN)
Format: 9999DDMMYY

where
first 3-digits represents a serial number
Followed by a 1 digit control digit
Followed by the date of birth

Because it contains the birth date, it is considered a privacy-sensitive number. For that reason, its use is restricted by law to certain areas of health care, social security, taxes, education and other administrative areas.

Exception: For those dates where the serial number has been outnumbered, the month 13, 14 or 15 is used!

The other system is a sector specific identification number.
Bulgaria:

Name: Единен граждански номер, Edinen grazhdanski nomer, (ЕГН or EGN)
Format: YYMMDD9999

Where
It first starts with the date of birt (20 is added to the month if the person is born before 1900, 40 is added if the person is born after 1999)
Followed by a 3 digit serial number, odd numbers for females! and even for males!
Followed by a 1 digit control number

Croatia:

Name: Osobni identifikacijski broj (OIB)
Format:99999999999

where there are 11 random digits and the last number is a control digit

Macedonia:

Name: Единствен матичен број на граѓанинот (ЕМБГ) /  Unique Master Citizen Number
Format: DDMMYYY999999

where:
the first 7 digits represent the date of birth, with a 3-digit year indication
followed by a 2 digit registry number, indicating also the place of birth
followed by a 3 digit serial number where 000-499 represents males and 500-999 represents females
ending with a control digit.

Montenegro:

Name : Jedinstveni matični broj građana/Јединствени матични број грађана, acronym (JMBG)
Format: DDMMYYY999999

where:
First 7 digits represent the date of birth (year has 3 digits)
Followed by a 2-digit (political) region code
Followed by a 3 digit serial number (where 000-499 represents males and 500-999 represents females)
ending with a control digit (based on a modulo 11 algorithm)

Serbia:

Name: Јединствени матични број грађана (ЈМБГ)/ Unique Master Citizen Number
Format: DDMMYYY999999

where:
First 7 digits represent the date of birth (year has 3 digits)
Followed by a 2-digit (political) region code
Followed by a 3 digit serial number (where 000-499 represents males and 500-999 represents females)
ending with a control digit (based on a modulo 11 algorithm)
Bosnia:
Name: Jedinstveni matični broj građana (JMBG)/ Unique Master Citizen Number
Format: DDMMYYY999999

where:
First 7 digits represent the date of birth (year has 3 digits)
Followed by a 2-digit (political) region code
Followed by a 3 digit serial number (where 000-499 represents males and 500-999 represents females)
ending with a control digit (based on a modulo 11 algorithm)
Romania:

Name: Cod Numeric Personal (CNP) / Personal Numeric Code 
Format: 9YYMMDD999999

where
The first digit epresents the gender, a century indicator, and an indication if you are born in Romania.
Followed by the date of birth
Followed by a 2-digit political region code (1-52 or 99)
Followed by a 3-digit serial number
Ending with a control code based on a modulo 11 algorithm

The first digit encodes the gender and the century of birth as follows:
1 male born between 1900 and 1999
2 female born between 1900 and 1999
3 male born between 1800 and 1899
4 female born between 1800 and 1899
5 male born between 2000 and 2099
6 female born between 2000 and 2099
7 male resident
8 female resident

The Netherlands:

Name: burgerservicenummer (BSN)
Format: 999999999

A nine digit number that can be checked with a variant of an modulo 11 algorithm
Winfried van Holland
CTO
Slovenia:

Name: Enotna matična številka občana (EMŠO)/ Unique Master Citizen Number
Format: DDMMYYY999999

where:
First 7 digits represent the date of birth (year has 3 digits)
Followed by a 2-digit (political) region code
Followed by a 3 digit serial number (where 000-499 represents males and 500-999 represents females)
ending with a control digit (based on a modulo 11 algorithm)
Portugal:
In Portugal, there are three main identification numbers: Identity Number, Fiscal Number and Social Security Number. All three are mandatory. In recent years the three different cards were substituted by a single card named Cartão do Cidadão with all three numbers and the voter identification number.
Hungary:
There is offically no identification number

There is however something National Identification Number
Format: 9YYMMDD9999

where:
The first digit represents the gender (odd for male, even for female) and an indication for the century and if persons are born outside Hungary
Followed by the date of birth
Followed by a 3-digit serial number and
Ending with a control digit

The meanings of the first number:

   1. male, born between 1900-1999
   2. female, born between 1900-1999
   3. male, born before 1900 or after 1999
   4. female, born before 1900 or after 1999
   5. male, foreign citizen living in Hungary, born between 1900-1999
   6. female, foreign citizen living in Hungary, born between 1900-1999
   7. male, foreign citizen living in Hungary, born before 1900 or after 1999
   8. female, foreign citizen living in Hungary, born before 1900 or after 1999

Slovakia:

In Slovakia there are currently two kinds of National identification number in use

Name: Rodné číslo (RČ) / Birth Number
Format: YYMMDD9999

where the first digits represent the date of birth, for females the month is increased with 50
followed by a 4  digit serial identifier.
The complete number must be divisible by 11.

Exceptions:
As the serial numbers are repeated every century, the number will not be unique!


Name: Číslo občianskeho preukazu (ČOP) / Citizen's Identification Card Number
Format: AA 999999

Where it starts with two characters followed by a 6 digit serial number.

Note 
This number is linked to the identification card and not to the person, people will change their number the moment they change cards.
Only for citizens 15 years or older
Czech Republic:
In Czech Republik there are currently two kinds of National identification number in use

Name: Rodné číslo (RČ) / Birth Number
Format: YYMMDD9999

where the first digits represent the date of birth, for females the month is increased with 50
followed by a 4  digit serial identifier.
The complete number must be divisible by 11.

Exceptions:
As the serial numbers are repeated every century, the number will not be unique!

A newer system is 
Name: Číslo občianskeho preukazu (ČOP) / Citizen's Identification Card Numbers
Format: 999 999 999

Poland:

Name: Powszechny Elektroniczny System Ewidencji Ludności (PESEL)
Format: YYMMDD99999

Where
The first 6 digits represents the date of birth
followed by a 3 digit unique serial number
followed by a gender identification (odd for males, even for females)
ending with a parity digit