San Andreas
In San Andreas there were a total of 6 girlfriends who CJ could date. You could take your girlfriends on various dates to earn their respect and eventually unlock their special ability. Each girl had a specific taste in men and you had to meet their requirements before she would agree to go on a date with you. For example one girl would like muscular men whereas another girl would prefer fat men. This meant you had to train at a gym to build up some muscle or eat a lot of food to put on weight. Each girl also has their on preference in dates. Some girls jst want to be taken for a drive whereas other might want to go to a restaurant. If a date is successful the girl might invite you in for 'coffee'. The camera remains outside her house while CJ and his girlfriend have sex inside.
For a list of all Girlfriends including their location, time available, likes/dislikes, special ability, and their general info have a look at the San Andreas Girlfriends page.
In GTA4 things were toned down greatly from SA. The lack of player stats such as muscle and fat meant that girlfriends were much easier to get and less of a hazzle to keep. Yet again there are 6 girlfriends in GTA4. 2 of those girlfriends are part of the story thus become your girlfriend no matter what and the remaining 4 girls can be picked up by arranging a date through LoveMeet and Craplist on the ingame internet. There are more activities this time too such as Bowling, Pool, Darts, Drinking, Strip Club or a Comedy Club. The rewards for dating the girls are less useful in GTA4 though. Only the 4 girls you meet on the internet have special rewards. For example 1 girl halves the cost of clothing in the stores for 24 hours, another girl replenishes your health although it doesn't work during a mission. The only good reward is from Kiki who removes your wanted level if you call her.