I like a bit of story and challenge. With regards to challenge, the best games in my opinion are that ones which require you to think on your feet and learn new tricks during bosses etc, but when it's perfectly possible to finish them off one go (e.g. you can take a fair few hits to learn from your mistakes). There you are using your own wit and it's satisfying.
I really dislike attacks which cannot be avoided, or having to spend a huge amount of time just to get back to try something again with minimal chance of succeeding. My all time pet peeves are insta-kill events, which you are guaranteed to hit every single time and just learn them all. It doesn't require skill as much as it does pure patience.
I'm playing through dead rising 2 at the moment, right up my alley, but my god some of the bosses are annoying. The only real way of tackling them is mashing a melee weapon or attempting to use a gun, but they all run faster than you and drain your health in seconds, barely giving you enough time to heal. If you have a melee off, you will die. To top it off, you then have to spend a good 5-10 minutes just getting back to the bloody boss to try it again! It's just not good fun and things like that can taint games IMO.
A quick google reveals I'm not the only one to think the bosses are a bit 'off'.