First off, if you read the following and think, there was nothing wrong with the start of those games!! you may well be right. I'm great at finishing games. I must finish 90% of games I buy (not counting Stream *cough*) Ironically the problem I have is starting games. I tend to be lazy and don't read the instructions. I also don't give a game much of a chance to impress me. If it seems too slow, too complex or the controls are too clunky then I'm out. That said, here are my candidates:
Diablo I never played Diablo. I tried the demo, while in the depth of my Myth obsession, and, for me, it had that classic RPG problem of seeming very simple and uninteresting in the early stages. I couldn't believe, after all the good reports, that you just clicked on stuff to kill it and picked up gold. Luckily, I sense that I wouldn't have enjoyed the game even if I'd carried on. Loot games don't last with me.
Batman: Arkham Asylum This is the one where the game was least at fault. The controls seemed unintuitive to me and the first stages of the game are very linear. I stopped playing thinking, sadly, that it just wasn't the game for me. Fortunately, a few weeks later I tried again and found that I'd stopped playing seconds before the game opening up. I continued playing to the end and enjoyed it.
Deus Ex: Human Revolution Waxy faces, weird clothes, extremely dumb npcs and a relentless orange colour scheme turned me off from the start. The fact that, as Giant Bomb had pointed out, you could dart one guy, wait for someone to investigate, dart that guy and repeat until you had a pile of all the guards in the area, killed the notion of stealth for me. I'd play for a bit, put the game away, get it out again, be underwhelmed all over again and put it away. Finally I stopped playing 'for good.' Months later, in a lull between games, I gave the game a fourth/fifth chance and it clicked. I don't think I've ever gone from loathing a game to loving it so completely. I actually stopped myself from using cheap tactics and that may have helped.
Dragon Age: Origins I'm playing this on 360 (I know, I know) and have just gone through the process from horror, to acceptance, to begrudging respect (it's what inspired this thread.) Great character design and animation is a huge part of what I enjoy in games. When I started Dragon Age: Origins and found that all the characters were as stiff as a board, had heads that turned on some kind of a ratchet and kept their fingers splayed, as if they'd been told that something horrible would happen if, for a moment, they should let one finger touch it's neighbour, I was disappointed. I tried a few intro stories and was treated to some ropey old scenery and main characters who looked like their faces were moulded out of a crumpled piece of paper. This time I actually pressed on through the horror of it all and, slowly, the game grew on me. The dialogue, characters and weighty combat mechanics started to win out. The flaws are still there but the good things are out weighing them several times over.