In the good old times (before a full-time job, family life and training) I passionately played a number of games: role-playing games, card and board games. Here's a selection of my favorites...
"Das Schwarze Auge" ("The Black Eye" - no, the name doesn't translate very well) was one of the first German role-playing games (RPGs). The first edition rules very rather simplistic, and the material was focused on the DSA world of Aventuria and a little hokey. For example, the base set came with a thin black plastic mask that the game master was supposed to wear to conceal his intentions - scaaaaaryyy.
Later editions had a tendency toward micromanagement - characters had hundreds of skills and spells, each with its own level and aptitude; character sheets grew to several pages length, and character creation was a matter of hours (if one took it seriously - it was not as excessive as Rolemaster, though). Nevertheless it was a fun game.
Dungeons & Dragons was as far as I know the first successful fantasy RPG and left its mark on generations of geeks. Its successor (Advanced Dungeons & Dragons) offered a significant refinement of rules and remained the biggest brand name in the RPG business until it was superceded by the next version (which again bears the name D&D). The basic rules are so simple that new players can get into the game easily, and character creation is quick and painless. On the other hand, vast amount of material is available - source books for all character classes and alignments, tons of articles form various magazines, campaign boxes for different worlds like the Forgotten Realms and Dragonlance, etc. - such that one can grow into the game.
The main weakness of the rules is the rapid increase in power level - while a level-1 character can get killed by a thrown rock, a well-equipped party of level-8 characters can butcher their way through a flight of dragons without breaking a sweat. This often leads to a "physical" style of playing, such that AD&D and "Hack'n'Slash" are near synonyms for many players.
Another German RPG that gets game balance right very nicely: characters have depth without drowning in numbers, and can grow without turning into demigods. Support by external sources, while good, is not quite as good as with other games, leaving more work for the game master, but leaving more money in the bank account. All in all, this may be one of the best fantasy RPGs, and in retrospect it the reason I didn't get into it as deeply as other games was more coincidence than anything else.
A brilliant parody that translates the essence of fantasy RPGs into a card game: go down into the Dungeon, slaughter monsters, loot treasures, plot against other players, what else do you need? The cards are hilarious: monsters range from the Lame Goblin over the Stoned Golem to the Plutonium Dragon, all of whom have extremely cute artwork. The game is easy to learn, can be augmented by a number of expansions, and doesn't take too long - two to three hours. Luck possibly plays too large a role - the first one to pick up some strong items is hard to stop - but winning is secondary in this game anyway.
For a martial artist like myself, this is of course a mandatory game: a card game version of a merciless fight for lunch money, for ideally four to eight players. It's a free-for-all as players abuse each other with punches and kicks and hope that their opponent won't counter with a chokehold. Inferior players form alliances to stop stronger ones, stronger players team up to finish knocked-down opponents - definitely a fast-paced game that is a lot of fun - but only if you don't take virtual bitch-slaps personal.
This board game version of American Football was one of the few Games Workshop games one could play without running the risk of bankruptcy: the was the base game, the league expansion "Death Zone", a handful of teams and star players, not above a few hundred bucks all in all. That's probably why the game was discontinued - which is a pity, since the game is a lot of fun; the teams have significantly different traits and require different strategies, and although the success of spectacular actions is a matter of luck, the outcome of the game very much depends on the players' skill.
Carcassonne is one of the best out of a genre of board games in which the game board is constructed during the game, and players have to make the best use of new resources and opportunities. Players draw landscape pieces that they must add to the existing landscape to build large cities, long roads and extended meadows, and take control of them. Sometimes it is worthwhile to collaborate with others on a building project (with a view to possibly cheating them out of the profits), sometimes outright sabotage is the best option. The game is simple, but addictive, and takes less than an hour, such that several matches can be played in one session.