Ah Lucrecia. The one name we hear Vincent repeat over and over again. But why?
Well, if you read the summary or know the plot of FF7, you'd know that she was a scientist Vincent knew while he was a Turk. But is that all there was to it?
Oh no my friend, that is not all.
The details aren't exactly clear in the game, but here's what we actually see -
There is a brief scene of Vincent and Lucrecia talking near the Shin-Ra mansion. He takes her hand, but she pushes him away. He reaches after her, but she runs away.
Moments later we see Lucrecia and the creepy Hojo hugging nearby. Vincent sees 'em and goes off to angst about it. As he leaves he says, "If she is happy then... I don't mind..."
Later we see Lucrecia, pregnant and Vincent and Hojo are having a heated debate. Hojo has been injecting Lucrecia with alien cells for an experiment while she's pregnant and Vincent... well, needless to say he's not too keen on the idea.
Hojo then pulls out a gun and fires. Vincent staggers, then falls. When he wakes up with his new body he blames himself. He claims it's his punishment for not being able to stop Hojo and save Lucrecia.
Vincent and Lucrecia DO meet later in the game(if you do the right quests), but Lucrecia again pushes Vincent away...
And so... we are left to speculate... Here are a few of the more popular theories:
To me, this seems a little unlikely given how cold she acts toward him...
2. Lucrecia actually loved Hojo and didn't return Vincent's feelings.
This seems a little more likely, but holy crap, how can you resist the hotness?
3. Lucrecia loved Hojo, but when Vincent came along she couldn't decide, classic love triangle stuff. She put aside her feelings for both men to work on the experiments, etc...
Seems most likely to me... of course this is all speculation...