Generally speaking, I feel that a terrible game is a pock mark on my collection, so I don't want to own it.
Nevertheless, there are exceptions
1.) If a game is notoriously bad, like Superman 64, I wouldn't mind owning it just as a tribute to failure.
2.) Some games cross the "so bad it's good" line. With a few exceptions, these are almost always FMV games, but if I can get a good laugh out of a game because it is particularly tacky or trashy, then I'll buy it. I'm on the hunt for a copy of
Ripper at the moment for this very reason. That game has Walken and it has cowbell. I need it, even if it sucks.
3.) If a game sucked, but had an original idea, I will sometimes buy it. Part of why I collect games is because i have an interest in their history of game design ideas. Sometimes a game has a unique control scheme, an original storyline concept, or an unusual setting. The game may have failed on a whole, but I appreciate the attempt to innovate, so I will buy it as a kind of curiosity. I think Lifeline (PS2) is a good example. It is completely controlled by voice recognition software. It doesn't quite succeed, but it was an interesting failed experiment nevertheless. I
made this thread about failed experiments awhile ago if you want more ideas.
4.) I will buy a bad game to complete a series or collection. I don't like to collect every game for a system, because I feel that makes a collection lose its individual personality. I will sometimes try to collect every sequel of a series I like though, even if I don't like all the games in the series. Certain subgenres also interest me, and I'll try to fill in the collection with titles that fit that mold, even when the quality varies across games.