An example of a fairly simple arpeggio is Heart Shaped Box by Nirvana as it uses 3 string 'power chords' in a simple order. A pretty fiddly one is Street Spirit (fade out) by Radiohead as the string pattern is complex and you make left handed adjustments to the chords as you play the arpeggio.
Very Important: When playing an arpeggio you need the most stability possible for your right hand, this is achieved by resting the side of your hand on the string bridge at the body of your guitar- like a hand rail in the dark.