Here are two, infamous and simple riffs, try them out:

"Smoke on the Water" by Deep Purple

e|----------------------------
B|----------------------------
G|----------------------------
D|----------------------------
A|----------------------------
E|0-3-5---0-3-6-5---0-3-5--3-0

Note that the whole song is played on the thickest/deepest pitch string.

"Come As You Are" by Nirvana

e|-------------------------------
B|-------------------------------
G|-------------------------------
D|-------------------------------
A|--------0---0---------2------2-
E|0-0-1-2---2---2-2-1-0---0-0----

This song is played on the top two strings of your guitar. It looks hard but do it slowly at first and you'll have it in no time.