After Sonic CD she only made her appearance in Sonic Drift, Sonic R and Sonic the Fighters until Sonic Adventure, in which she was a fully playable character and had a completely new modern hairstyle.
The games she participated so far are:
Sonic CD, Sonic Drift, Sonic R, Sonic the Fighters, Sonic Adventure, Sonic Adventure 2 Battle, Sonic Heroes, Sonic Advance 1-3, Sonic Riders. (Also in the Sonic X episodes)
Amy pursues and wants to marry Sonic, but he ignores her and leaves alone all the time, however she doesn't give up.