I just installed Bitcoin Wallet for Android. It is quite intuitive. Took me 5 minutes to get familiar with it.
I made a backup with a strong password (12 random characters) and emailed the encrypted file it to myself.

But still, I don't feel that safe. Phones are subject to all kinds of security problems.

I've decided to keep 50 EUR in this wallet. If I ever come across some shop that accepts bitcoins I'll try it out. It is also good to keep some small money there just to see if it really is safe.