Ever had that happen? I remember I was insanely excited when I got my hands on the first Sims game, but once I started playing I very quickly became bored with it. As in, I only played for two/three days. Feeling kinda disgusted I proceeded to play something else for a couple of days. But then out of nowhere I suddenly found myself in the mood for another go at The Sims and so I installed it again. I couldn't get enough of the games for several weeks after that.

Probably every strategy game I've played. The first time I usually only get the basics. So it's the second time they start to get interesting.

I sometimes have this happen with RPGs. Thing is, I prefer knowing what's going to happen, especially when it affects the gameplay in some way (like whether the game lets you use a given character at any given point in the game). It also helps to know what the abilities of different characters/classes are and how they interact.

Of course, sometimes I discover things about the game on subsequent playthroughs that I didn't know before.

Shadow the Hedgehog. Hated it on my first few attempts, but it isn't that bad of a game even if the controls are a bit slippery.

Final Fantasy 8. The game is a lot better once you understand the junction system and break the game. Also the game has a lot of foreshadowing that's easy to miss the first time through.

There's others I'm sure but those are the two that immediately come to mind.

I was going to say chess, but that analogy works for strategy in general. Most people aren't into strategy and strategic planning because most suck at it the first time. Learning complicated movements and tactics takes time and energy, and you may fail the first time around. The intricate nature of strategy reveals itself gradually. The non-linear components take an early lead in the race.

Reminds me of Final Fantasy 2, which is a lot more fun when you realize that evasion is important and that equipment tends to interfere with status spells.

Also, I just remembered a good example: In some Might and Magic games, if you know where everything is, you can do things in unusual orders. In MM3, one could use one of the "cheat" mirror codes to get a bunch of money, then use it on fountains to take care of that dragon cave early in the game. In World of Xeen, clearing the Dragon Tower early is quite fun and will make the Labyrinth of Lost Souls, probably the most annoying dungeon combat-wise (fighting high-AC magic-resistant enemies is not fun), rather easy, thanks to being level 50 (or close to it) with access to a fountain that gives you +50 levels.

Ah, but the Sims is kind of weird like that. I'll play it hardcore for a couple of days, then put it away again for a month or two. Somehow it lends itself well to short but intense bouts of playing.

For me it's Dragon Age 2. I still think it's crap compared to Origins, but the first time I played it I was super disappointed with it, and I ended up hating it with a fiery passion. A year or two later I gave it another shot, and while it still wasn't a great game, I definitely found it interesting enough to keep going. I suppose my initial disappointment had to do with the fact that it was clearly not like Origins at all, and once I'd reconciled myself to that in my head it was easier to accept the game for what it was.

Red Dead Redemption

It took 3 tries before I could really get into it. I think it had to do with the fact that there is a lot of empty space in that game where nothing is really happening and the first 2 times I found that boring. On my 3rd try the game just "clicked" with me. I enjoyed the exploration, the prairie and the frontier atmosphere, the horse-riding, looking up at the stars at night etc. It's also about knowing what to ignore and what side missions to do. But it really is a good game.

I had this with GTA V. When I first bought it, I played it for 2-3 hours, then lost interest. For some reason, it just didn't click with me. So I left it alone for a while. Then about four months later or so, I thought I'd better give it a second chance, and suddenly it clicked. Then I plowed all the way through it to the end.

Yeah.
What probably defines a strategy player the most is not intelligence. It's patience.

I don't think it's ever happened with me with a strategy game, but perhaps that is because there's usually a very fun campaign to get lost in, which only very rarely requires you to master some of the tactics. Alpha Centauri might be an example though. The first time I tried it out I had no idea what I was doing, and I didn't hand around long enough to figure it out.

Depends on the campaign. If it throws you out on a open grand map I'm ok with it but I really don't like "standard" campaigns. All they do is lock features, lock the pace and force you to play exactly like the developers want.
That's not strategy it's puzzle.

Gimme large open and/or random maps any day. I'm really not a strategy campaign player.

DoW:Dark Crusade taught me that an 'open grand map' can be really fun. Dow 1 on the other hand with its far more standard campaign was pretty lackluster, except for the briefings of course, with Gabriel Angelos's ridiculously awesome voice :)

By the way, how about RTT type campaigns with levels that typically allow a far greater degree of freedom? Eg. Ground Control which has a pretty fun campaign, or World in Conflict with its totally kickass campaign.

Every RTS minus Cossacks which was so GODDAMN HARD I spent a week yelling at myself for actually trying to play it a second time! :P

Strategy games: You usually learn from your mistakes, e.g. exposing your unit to counterattacks.

Games with jokes: Sometimes you miss or don't get the jokes, e.g. because you lack context.

Adventures with complex storylines on multiple levels: Might concentrate on some storylines and don't notice something in another one.