Gee, erm...
I like the openings to these series:
Re:Cutie Honey- Mostly because I absolutely love the animation style and the song is nostolgic to me. Link: (May not be appropriate for younger children... There's no nudity but... Lots of ripping and tearing of clothes. :P)
http://www.youtube.com/watch?v=yM9_WHbm3OEGetsumen No Heiki Miina (Aka: Lunar Rabbit Weapon Miina)- For some reason, I'm really attracted to this song... It starts out a bit oddly pitched but I find myself humming the chorus of this theme song to myself at times. Link:
http://www.youtube.com/watch?v=3pAhIU9QK0kAlso, this is an ending to an OVA of one of my favorite comedy mangas but it's so extremely random so I thought you might want to hear it...
Link:
http://www.youtube.com/watch?v=oAdr94fzNPAThe anime is Dragon Half which is a fantasy-adventure spoof and It's just... Well... Random to hear the main character Mink singing about Eggs and tomatoes...
Other openings I like:
Spice and Wolf Season 1 OP
Windy Tales OP
Astarotte No Omocha OP
Urusei Yatsura OP
Geez, this turned about to be a long post...