Velocity can change without speed changing. This occurs in circular motion, where the velocity vector changes continuously while speed is held constant. Examples include a tetherball on a string, a car going around a curve at a constant speed, and an object in a circular orbit.
You have to remember that in physics and maths, acceleration means:
1. speeding up or
2. slowing down or
3. changing direction
(or a mixture of 1&3 or 2&3).
That's because velocity is a vector (has magnitude and direction) and acceleration is how fast velocity changes.
(This is different to the non-scientific use of the word 'acceleration' which simply means speeding up.)
So, as @Drakkith notes, for something going in a circle at a steady speed, the velocity is changing (as the direction of velocity is constantly changing). This is classified as 'acceleration'.