My daughter is a finger-sucker. When she was born we gave her a pacifier (paci), then at about 2 months old she discovered her thumb and could get herself back to sleep - we didn't argue at all. Then she swapped to sucking the middle two fingers of her left hand.
She's done it ever since. She's doing it right now. It's very sweet, but it's also very annoying.Her fingers are starting to look funky and I fear for her teeth.
We're tried bribes, we've tried paint-on yucky junk, we're tried rationalizing (because you know, rationalizing with a 3-year-old is a great idea). Nothing works, and I'm starting to wish we had kept with the paci so that we could take that away. We can't cut her fingers off.
But for now, she's still sucking her fingers. I guess it's okay for now, I mean - she is only three. And it's one of the very last things left that connects her to the baby she was. She's so grown up otherwise. *sigh*