Here are a couple of easy ones I use.
An 8-note pattern: Use strings 4-1 only (D, G, B, e). Use thumb on 4, index on 3, middle on 2 and ring on 1. Pick 4-3-2-3-1-2-3-2. Play whatever chord you like with your left hand and it should sound OK. When you get proficient, switch your thumb to the string (6, 5 or 4) which frets the root note of the chord. I use this for Behind Blue Eyes (The Who) and Love Hurts (Nazareth's version).
A 7-note pattern: Again, with strings 4-1, simply 4-3-2-1-2-3-4. I use it for Everybody Hurts (REM) with a little variation on the walkdown G to Em.
Some advice from someone who is just above rank-amateur at fingerpicking: If you want to do it, learn a lot of different styles and patters. Otherwise, all of your songs will sound alike.
Practicing these simple patters will prepare you for learning more complex and song-specific ones, such as More Than a Feeling (Boston) and Dust in the Wind (Kansas).
Good luck,
'Nomikal
"Just because you've always done it that way doesn't mean it's not incredibly stupid." - Despair, Inc.