Velma Dinkley is a founding member of Mystery, Incorporated. She is the smartest of the group, though she feels under appreciated. She's rather bold, and gets along well with Daphne, in whom she finds a mutual support.
Velma was with Mystery, Incorporated before moving to DexLabs. While they were working together, Dexter began to have romantic feelings for her, which were unreciprocated. Feeling uncomfortable, she decided to relocate to Retroville to work alongside Jimmy Neutron and Rook Blonko. Her current project is to fix up Bobert.
Cartoon Network poked fun at a possible relationship between Dexter and Velma (although it's one-sided). Here's the video that shows it: video
Whether or not she still has feelings for Shaggy isn't stated.