I would be interested in hearing opinions on this, but since no one actually reads my blog yet, I will go ahead and give you mine. Some items that make a game fun are creative design, likable theme, replay value, risk-reward ratio, and challenge.
Creative design is important, especially in board games and video games. Table-top
RPGs rely a lot on imagination, so its not as big a factor there. But regardless, a visually appealing game goes a long way. Like people, a good looking game can still be ruined by poor mechanics or content, but if we are going to look anyway it might as well be good looking. Talisman and Mousetrap good examples of games with great creative artwork.
Likable themes can make or break games. There are a lot of games with elves and dragons out there because we like those themes and expect certain things from them. The same is true for space games, war games, and so on. Themes need to tie in with the mechanics as well.
Catan wouldn't work well with a cowboy or Eskimo theme, but it works great with the settlers theme. Monopoly is a good example of a game that has come to fit many MANY themes.
Replay value is also very important. Lots of games are fun the first time, but a good game keeps you coming back for more. I
particularly appreciate Small World in this area. Because the races and powers are changing each time you play, you have to come up with new strategies every game.
Risk/reward goes with mechanics. No one wants to play a card game or dice game that you put together a complicated strategy together for, only to end up with the same reward as the 8 year old collecting simple things. Ten thousand or Hand and Foot are good examples of games where risks can be
devastating or rewarding, and that makes those games fun.
Challenge is last because it varies more than the others. Challenge is often what
separates games into age groups. Snakes and Ladders is a kids game because it has no challenge, and Candy Land is only for "All Ages" because it is completely based on luck. Chess and Risk are "grown-up" games because they require lots of rule knowledge and adult strategies. It is difficult to find games that challenge people of all ages, but if you find a game that is challenging for everyone playing than you have a lot of fun. Deal or No Deal has a lot of imagined strategies, yet for the most part it is just as much a game of luck as Candy Land, yet all ages enjoy it.
If you don't know about any of the games I have mentioned, feel free to ask and I will explain.