On the subject of the first movie: "Vacation". It will never leave your head ever.
Oh GOD are those Italian themes addictive! Probably one of the best examples is the one for the Johto season. (Gotta catch'em all)/You gotta catch'em aall! You gotta catch'em aall! You gotta catch'em all! ALWAYS POKÉMON!
No song in the series comes CLOSE to the amount of sheer rockitude and badassery of Pokemon Advance Adventure. Its so amazing, its one of the only songs 4Kids decided to keep from the original version.
It may not have been a part of the series proper, but I have had Don't Say You Love Me stuck in my head off and on for approximately seven years.
Aside from the already mentioned Pokeraps, the Hoenn Pokerap. "P to the O to the K to the E M O N!"
The US Diamond & Pearl first season opening. "Pokemon! Po-ke-mon! It's all about the challenges...."