Sat42: Careful not to simplify too much: fun is fun, and it takes different sorts. I prefer a 7/10 (good) RTS game over a 9/10 (excellent) sim racing title any day of the year. If you are particularly interested in storytelling, you might play a game for its strong narrative even if the overall package is comparatively less good (e.g.:
Geneforge). My 'minimum' required general rating for a game can fluctuate depending on the genre, but generally I decide to play a game if I have reasonable confidence that it will be at least good.
Now of course your last sentence says 'you might like a
low rated game [...]' and in truth, an actually overall low rated game - not just relatively but actually falling into 'negative' territory in aggregate, i.e. below 5/10 - I have never found myself liking such an example of a game. I have played two such games:
AD 2044 (got it for free) and
Pax Corpus (free too!) and I agree they provide a mostly a negative experience. I have also played some old school titles that were highly regarded in their day and which I would rate below 5/10 (best example is
Shadow of the Beast II) but that's another story...
If you don't limit yourself to thinking of 'low rated' as actually falling below 5/10, then you can start looking at titles that were
disappointments as opposed to actually bad, those that got middling reviews rather than actually negative ones, and those can actually be fascinating depending on taste (not to mention: they may improve significantly way after their original release dates).

Magnitus: I think different people have different thresholds of "good enough". For me, it's 7/10 or above (although anything below 8/10 will have to be heavily discounted for me to consider it). For others, it might be 5/10 or even less (though probably because of cultural bias, most would probably consider a game rated below 6/10, which is the passing grade in most schools I think, a bad game).
The lower you go, the more you have to be an outlier to disagree with the popular consensus though (and lets not forget that we are talking about a "great" game here, someone who would rate a game 6/10 might consider it okay, but certainly not great).
For the genre, sure, there are some genres that I like more than others and some (very few) that I simply won't touch no matter how well rated the game is, but like lupineshadow here, I'm heavily biased towards ratings.
Life is short and I don't mind getting out of my comfort zone a little and enjoy a best of breed game in a genre I tend to enjoy less rather than have a rehashed average experience in a genre I tend to like more.
I basically agree.
Magnitus: I do think that my single biggest bias is innovation though. I'll tend to be more forgiving of a game that went for the stars and fell short than a game that played it safe to the point of being considered average at best.
Same here. I listed
, which is the epitome of 'playing it safe' and being average as a result, with a journalist saying it "should have shipped in a plain white box with 'Realtime Strategy Game' stamped on it."), but another example would be
(Playstation version) more out of 'morbid curiosity', not because I thought I'd have a decent time with them. Sometimes the 'video game archeologist' aspect takes over me!