There were a bunch of characters and they went with the different flavors. Off the top of my head, they were:
Chucklin' Cherry
Smarty Arty O
Mean Green Puncher
Rockin Red Puncher
Berry B
Some sort of grape guy
In 1993 they had collector's checklists on the back of the labels so you could get every character in every color. I actually suceeded, filling up a paper box with this stuff. They all got recycled eventually though.
In the late 1990s at the end of the Squeezit's run they also had color-change Squeezits. It would start out as, say, blue. You'd put a little drop with only the finest in artificial coloring ingredients in the top of the bottle and watch it become, say green! These came in clear bottles.
Kool-Aid made Kool-Aid Bursts, a similar bottle filled with Kool-Aid but minus the characters. There was also Mondo, who had the bottles but weren't as easy to squeeze.