CPU Olimar's AI forces him to stand still when you do so in front of him.

[ThatGuyYouMightKnow]

If you stand still in front of CPU Olimar at a certain distance (or at least don't move, you can take actions), he'll stand still as well.

This also happens with Donkey Kong, as far as I've tested.

Staring contest.

(Didn't see this posted anywhere else)

 

[KFrosty]

There is a whole thread made for the bad AI. Someone does mention Olimar's pacifism on the second post.
http://smashboards.com/threads/just-a-few-ai-fails.343652/

If you feel like there is more to add, you should put it there so that multiple "Bad AI" topics aren't constantly building up