Why do you replay your favourite games so often?

I like strategy, tactics, planning and management. I also like to do hidden stuff, IF I am against another player.
I don't like gambling. Nor do I like determinism or puzzles for a game. But a small risk is nice to have.

As for theme's. A complete new world is my favourite. Where a certain odd part is explained in detail and logic. A story is great, especially when the setting is placed and the problems start later on.

I hate solitaire games. Or the AI has to be good.
I don't like 1 v 1 games, once one player gets the upper hand, these games are not played any more. But coop are the best with at least 2 players.
3 or more players is what I prefer. Because then 2 on 1 is possible if that one player is too strong.

More importantly, I am an advocate of helping a weaker player. Thus if one player falls behind, some help is appreciated towards that player.

If a game has dis-functional parts. I don't like that game in particular. Every aspect has to have it's use.

My current favourite game to play with others is Incan Gold. It's easy to teach to someone new (even those new to tabletop games), the theme is accessible, and the seemingly simple choice you make has HUGE, dramatic consequences. It's a game where everyone is involved and even when there's a runaway leader no one really feels so bad about it since it's a game that's still captivating while obviously so dependent on luck of the draw.

"Stay or Go!" is the unofficial name of Incan Gold, as we eventually chant, "Stay or go...Stay or go..." when we start round 3 or so.

The game is brilliantly realized, and it's some of the most fun I've ever had with board games.

It's all about the experience. I don't necessarily have a favorite mechanic or theme; I love or hate a game based on what kind of experience it creates.

Without a close second, the game I play the most is Dominion. It has these aspects, which make it a greatly replayable game. These are not in any particular order.

One game takes just under an hour. (I play at lunch at work a lot.)

The basic mechanics are easy to learn.

Every game is different. Even once you know all the cards (I do) then a new game offers a new combination that requires you to figure out a new strategy. The cards are well designed so that the best strategy will usually be a combination of cards, as opposed to a single-card based strategy, so those combinations are important.

Some cards seem to be of little use by themselves, but work amazingly in combination. (Example: Rats and Apprentice and a cheap +buy card.)

Excellent balance of skill and luck -- about 75/25.

Excellent balance of strategy and tactics -- about 70/30. (The correct value for this balance is more opinion-based than the others in this list. This is a perfect balance *for me* but others might prefer a game to be more or less strategic than this. OTOH, TransAmerica is probably 40/60 and I love that game, too.)

Usually a good balance of player interaction vs. players working on their own strategy. However, with some card sets, Dominion is properly criticized for being just "four-player solitaire." This is probably the biggest point against Dominion, but I can recognize those games before we start, so we just re-run the randomizer and skip those. Puzzle Strike is a similarish game to Dominion but has more interaction built into the base mechanic. I don't like it as much, though, because it doesn't hit as perfectly on some of these other elements.

Even with a given set of cards, there are usually multiple viable strategies. Your best strategy is somewhat influenced by luck and somewhat influenced by what it looks like your opponents' strategies will be, so it is important to be flexible, but not so flexible that you have no direction.

There is excellent decision tension, but almost never enough to cause analysis paralysis. This is achieved by giving the player frequent occasions to make a choice, but relatively few choices to pick from at any one time. (This point might be the most important one in this list.)

In every game there is a clear transition: You go from building your engine to exercising it to earn victory points. Knowing when to make this transition is an important strategic choice.

My collection is still small. For now Lords of Waterdeep, A Touch of Evil and Fortune and Glory are my favorites.

A strong theme is definatly something that draws me in. It can make a boardgame a true work of art to look at.
I tend to be disappointed by games that have amazing and imaginative box art, but the actual game components looking very basic and simplistic.

Of course it needs to be combined with fun gameplay though, that is a mixture of strategy so that decisions matter, and a bit of luck to keep a random factor in it.

Replayability is important too, I like it when games are different each time.

Lords of Waterdeep remains reasonably similar I suppose, but the starting quests are random as well as the intrigue cards and your lord will be different too so thats different enough for me. Different buildings available too.

But Fortune and Glory is far more different even. The rules are more complicated too and require the occasional peek at the manual but I know the rules quite well by now.
There's 12 heroes to choose from which all play differently, the treasures and their locations are random, the danger deck is quite big since I have the card expansions which also adds deadly tests that are harder to pass.
Can also play it coöperatively against a vile organisation, and competitively with or without a vile organisation.
Each vile organisation also makes for a very different experience.
So yeah, lots of replayability. I wish I could play this game more often.

A touch of Evil might possibly be even more varied. Also requires the occasional peek at the manual but most things do speak for themselves.
This one I have complete with all expansions.
Which makes for 24 heroes to choose from, 14 villains to hunt down and fight, three linked game boards of which the expansion boards are optional, each location having their own unique deck of cards to draw and many decks being quite big due to all card expansions.

I greatly admire flying frog for putting together such wonderfull thematic games, and I am aiming to make a somewhat similar experience, but less complicated, and many changes to suit it more to my taste and the fantasy theme I am going for.

Some games just land in that perfect nexus of great story, exceptional production, and fun to play. "Battle for Middle Earth 2", "Homeworld 2", and Ratchet & Clank 2" (got a thing for sequels I didn't realize...), "Mass Effect 2" all killed it in my book and I played through each over half a dozen times.
Each one just had such great production value I could write a thesis on why each one dominates their predecessors.
"Rune Wars" and "Elder Signs" too have great narratives and are fun to play while demanding a good deal of strategic thinking. I guess about all these games is that there is a level of strategy to each (maybe not so much R&C - but man it had alot of pretty colors and lights) but none were overly technical...the flipside would be a game like "Last of Us".
I love that game so much for the story and environment it created. Naughty Dog did such an excellent job of putting you in their world that I get excited everytime I get to tell people about the game. However, it was too slow and tense for me to go back and play again, even though I REALLY enjoyed it and kinda wanna just watch the story unfold again.
Fun question to reflect on! Thanks for sharing.

My initial reaction is that I play my favorite games because I know them.
Duh.
I'm much less inclined to learn a new game when a familiar game that I like is available, especially if the new game has a steep learning curve.

What I like in games (once I've gotten over the initial hurdle of learning them) is a simple rule set and not a lot of moving parts but where a satisfying amount of investment can still occur.
I don't want to play games with a lot of busy-work, bookkeeping and cube pushing that feel more like doing taxes than playing a game. That knocks pretty much any heavy euro off my radar. :)
I also tend to shy away from conflict and competition. I tend to root for my enemy and point out cool combos they can pull off if I think they missed it. I want to win, but I'm okay with losing if I can high-five my opponents because of a sick play.
Some of my favorites that I own that I would put in that category are Incan Gold, Tsuro, Gravwell, Ricochet Robots, Balderdash and Dixit.