I'm one of those self-taught guitarists. When I was first learning the instrument, I imitated a friend's version of Travis picking wherein she used her thumb and 3 fingers (index, middle, ring), rather than the more traditional method (thumb and first 2 fingers). So, with the thumb (t) positioned to play alternating bass notes on the 4th, 5th and 6th strings, index finger (i) on the 3rd string, middle finger (m) on 2nd string and ring finger (r) on 1st string, I pick the following:
(using Roger in Baltimore's notation style with slashes between each beat of the measure and commas between "half-beats" a.k.a. eighth notes):
4/4 tr/i,m/t,r/i
...or, for a slightly fuller sound on the downbeat:
4/4 tmr/i,m/t,r/i
I find this useful for open chords such as E, A and C where the root of the chord (the bass note that the chord is named after) is on the 5th or 6th string. For open chords like D, where the root is on the 4th string, I sometimes revert to traditional thumb-and-2-finger Travis picking so that I can use my thumb to play alternating bass on the 4th and 3rd strings as well as the 4th and 5th strings.
Sometimes I even Travis-pick using all 5 digits, with the pinkie (p) positioned on the 1st string, r=2nd string, m=3rd string, i=4th string, t=5th or 6th string:
4/4 tp/i,m/t,r/i or tp/i,m/t,p/i
...and, again, more strings can be plucked at the same time especially on the downbeat (such as trp or tmrp).
Actually, I do a lot of that plucking-of-multiple-strings-at-the-same-time as part of my playing style, mostly like this:
4/4 tmr/i/tmr/i or tmrp/i/tmrp/i or tmr/i,m/tr/i
For this reason, people tell me my style reminds them more of piano-playing than guitar-playing. But I do strum, too! Alternating picking and strumming within the same song (or even in the same measure!) is another way to vary your accompaniment.
There is a LOT of very good advice in this thread, but I think the most important is the tip that one should not get so bogged down with the learning of new techniques that one forgets to have fun! That said, it is still useful to "teach" one's body and brain to perform a picking pattern more or less automatically and then vary the patterns to keep your accompaniment fresh-sounding. Of course, such rote learning is not much fun, so to prevent boredom while playing a pattern over and over as you "teach" yourself the finger movements, get into the habit of practicing these patterns when you are watching television (this also helps with learning to forge ahead and keep playing despite dissonant background noise -- a skill that comes in handy when performing in public and can keep you from feeling distracted by crowd noise).