Below are some common student misconceptions about the concept of velocity:

Velocity must be positive. (description) (discover) (references)

Same position means same speed. (description) (discover) (references)

Leading (following) particle moves at a faster (slower) speed. (description) (discover) (references)

Same velocity means same acceleration for two objects. (description) (discover) (references)

Larger (smaller) velocity means larger (smaller) acceleration. (description) (discover) (references)

Zero velocity means zero acceleration. (description) (discover) (references)

A positive slope for a negative velocity means the object is speeding up. (description) (discover) (references)

Students plot position and velocity graphs as the path of the particle. (description) (discover) (references)

Velocity is intrinsic to a particle, and doesn't depend on the observer (i.e. the ground is a preferred observer). (description) (discover) (references)