I try to have seen the movie too, but that's not a hard rule. In the past, I have bought posters for some obscure films that I then made a point of tracking down and watch. This is actually part of the fun for me: discovering new movies after I came across their posters. I would estimate that I've seen about 90% of the films that I own posters for.
While I tend to gravitate towards posters of films that I like, I don't particularly worry about the movie in question being "good": many terrible movies (particularly 1950s B-movies) have fantastic poster art, while I can think of a few classics with less-than-inspired artwork that I personally wouldn't touch. I'm much more interested in the visual appeal of the artwork than the actual quality of the movie in question.
I mostly collect larger sizes (US one-sheet, 3-sheet and 6-sheet, French 47x63 and up, Italian 2F and 4F, UK quads), as I'm not interested in US inserts, lobby cards, window cards, etc... Once in a blue moon I will buy a half-sheet if the design is different/more interesting than the one-sheet, but I typically don't seek out those very much.
My other general criteria is the time period: I mostly collect paper from the 1930s all the way up to the mid-1980s, with a big focus on the 1940s, 1950s and 1960s. I was born in the 1970s but somehow I'm much more drawn to movies from earlier decades, go figure! I really don't care for any of the modern posters aside from a few rare exceptions.
Since I'm interested in earlier periods, I'm quite flexible about condition, as it can be difficult to find an 80 or 70 year-old poster in pristine state (this is particularly true of the lesser quality of Italian paper, which tends to be especially brittle). I actually don't mind a bit of wear and tear, as to me that's part of the poster's history.
Like Thierry, I really much prefer a folded copy and will only reluctantly buy a linenbacked poster if I really can't find an unrestored example otherwise. Although I have relented in recent years and have started to acquire more linenbacked examples, I have done so for large format only, and as a result I don't own a single one-sheet that's not folded. I can get behind the concept of linenbacking in those cases, as it is convenient to have a poster that was printed in 2 or more separate pieces held together by one single support (particularly in the case of those pesky old Italian 4F and their brittle fold lines!).