Finches

Finches are smallish birds with biggish triangular (ish) beaks. Besides the birds with "finch" in their names, this group includes grosbeaks, cardinals, and tanagers, which tend to be a little larger. Crossbills are in this group, and their beak is a bit different. I've not yet seen a crossbill, nor a liwi whose beaks are even weirder.

American Goldfinch The Goldfinch (American) is one of the classics that comes to my mind when someone says "finch"