1) The all I know are:
Ge-Ge-Ge no Kitarō Season 5 OP2 (ep.27-51): Yōkai Yokochō Ge-Ge-Ge Bushi
In each episode, two different monster characters are introduced in OP animation
and song. Therefore the combined total duration of the OP song is very long.
http://www.nicozon.net/watch/sm2401168 (AMV with a part of it. Click the sumnail then a playing window will come up. You can disappear the comments by clicking a right bottom button.)
Dragon Quest: Abel Yuusha
Not in each episode, but ED animation changes little by little. Some of them are:
http://www.youtube.com/watch?v=04_cbzY4Asg
http://www.youtube.com/watch?v=_5ncycAJTR4
The Simpsons
Opening animation slightly changes in each episode.
http://en.wikipedia.org/wiki/Couch_gag#Variations
2) Some of the result of googling (with brief translation of the description):
Pokemon Series
Animation changes everytime the characters get a Pokemon, get it evolve or separate with it. Because the change can be very slight, viewers may not notice it at a glance.
Natsu no Arashi!
Lyrics of verse part changes in each episode OP.
Pani Poni Dash!
An elaborately planned anime including OP song in which the lyrics of verse part changes in each episode, its unique camera work, OP/ED/Eyecatch illustration/Endcard which changes in each episode, and many use of parody from movie, manga, anime, game, etc.
Tsukuyomi - MOON PHASE
OP animation slightly changes in each episode and it contains shiritori game.
http://www.aniza.net/tsukuyomi_op/
http://sishou.seesaa.net/article/2043380.html
http://sishou.seesaa.net/article/2075276.html
Bokura ga Ita
ED song changed often to make it suit the theme of each episode.
Sora no Otoshimono
ED song changed every week.
Black Jack
It's likely that different characters come up in OP animation depending on each episode. (Not sure)
Ef: a tale of memories
OP animation changes in each episode.
ARIA
OP animation features the summary of each episode.
Sketchbook - full color'S
Every OP has a different character depending on the episode. And OP song changes in ep.12.
Sorry if they contain wrong information. According to some sources, an animation studio Shaft is likely to be good at these kinds of things such as Pani Poni Dash!, Natsu no Arashi! and Ef. So I would suggest you check the rest of their animes as well.