Rex, agreed -- I find if I can whistle a tune all the way through, I can learn it faster on the fiddle and move it to other instruments without too much trouble.

Stringsinger, I feel like we're in a similar boat with the fiddle, so here are some of my favorite easy tunes:

The Eagle's Whistle (http://www.thesession.org/tunes/display/4192)
The Earl's Chair (http://www.thesession.org/tunes/display/221)
Rolling Waves (http://www.thesession.org/tunes/display/88)

And, for fun with tone, Mo Ghile Mear (http://www.thesession.org/tunes/display/1612)

I have recordings of "The Earl's Chair" and "Rolling Waves" that are good to learn from, if you like.

Cheers,
Megan