First off, Dango Daikazoku from Clannad. This song will get in your head and won't leave. Ever. Animation is very cute and relaxing. I also like how they used similar variations of it as background music in the anime.
The next one is Kesenai Tsumi from the Fullmetal Alchemist anime, season 1 ending. What I liked the most from the song is the bass, and the song itself is very catchy.
Finally, Futari ha Wasurechau from School Rumble. It is very relaxing, similar to Dango Daikazoku from Clannad.