Woody's main squeeze is Bo Peep, a porcelain figurine based on the nursery rhyme character who, with her sheep, is part of a lamp in Andy's room. Does a lady on a lamp count as a toy? In Andy's room, definitely.
It's clear right away that Bo Peep and Woody have a serious flirtation going on. Bo even offers to get someone else to watch the sheep one night. Smooth, girl. She's also one of the only toys that stays loyal to Woody throughout the movie. When everyone in Andy's room is trying to attack Woody for pushing Buzz out the window, Bo Peep comes to his defense.
She also doesn't like it much when Mr. Potato Head refuses to help Woody while he's trapped in Sid's house. When they all find out that Woody has brought Buzz back to them, Bo springs into action to rally the other toys. Yup: Bo is as caring and loyal to Woody as she is to her sheep.
Of course, for all Bo Peep's objections, she doesn't actually succeed in doing anything to help Woody. She may be smart and sensible and put up a good fight, but, in the end, it's not enough to help Woody when he needs it. This lady—who's the main female character in the film—ends up being pretty ineffective.
But, hey, how much can you really fight when you're literally made out of porcelain?
Here's a fun fact: Bo Peep was originally supposed to be a Barbie doll. Joss Whedon said he wanted Barbie to be Woody's girlfriend and to ride into Sid's yard in her pink corvette and save the two toys at the end of the movie. But Mattel wouldn't license Barbie for the movie because they didn't want Barbie to have a defined personality on film. They also thought the whole thing might flop.
Obviously, they changed their minds since Barbie shows up in both Toy Story 2 and Toy Story 3.