Essentially, if there is some collection of proper techniques that have distinct rules or characteristics about them, that's what I'm looking for. There's not one particular artist or type of music I want to play, I just want to know how to recognize styles when I see/hear them. Or is it more common for a style to be associated with a specific player, like Lightnin' Hopkins or Rodrigo y Gabriela?
Assuming you're not interested in classical-style fingerpicking (which is an entirely separate subject), there are no set "rules", per se. Folk-style fingerpicking, like folk music generally, is a product of people figuring out how to make the music they want to make, without necessarily caring too much about orthodox conventions.
That said, probably the most widespread style of fingerpicking is called "Travis Style", named after Merle Travis. In Travis style, the thumb plays an alternating bass note on the quarter notes while the fingers (maybe just one, maybe all four, depending on the player) play a melody line, often syncopated, on the top three strings.
Bob Dylan's "Don't Think Twice, It's Alright" is a good example of Travis-style picking---there are hundreds of other excellent examples too, of course, but I picked this one because most people have heard it. Here's the tab for the first two bars (it's capo'd at the 4th fret). The thumb plays the first five notes, which are all bass notes:
(still trying to get the hang of this jTab thing)
Doc Watson, Mississippi John Hurt, and many, many others also primarily played in a Travis picking style, but it's definitely not the only way to go.
Modern fingerpickers do pretty much whatever they can to get the sounds they want out of the guitar. Michael Hedges is the probably the most well-known example of a fingerstyle player who used all sorts of unorthodox techniques, including tapping, slapping, using a looping pedal to lay down a background part that he could then play live over, etc.
Leo Kottke is an interesting example of how technique influences style. When he was younger, he played using a more folk-style technique, but eventually that gave him tremendous hand and wrist problems. So he switched to a more classical-style technique, which is more ergonomic and has resulted in a slightly different sound for him. He can still play all of his old stuff, of course, but it just sounds different, and it seems as though the new technique has influenced his songwriting, too.
You can take a classical style and incorporate it into your playing in a different idiom: See: Joe Pass or Steve Morse (who also is/was a master of pure classical finger picking as well). See the first four albums by the Dixie Dregs....
Also a combination of Flatpick and Fingerpicking is an oft used style : See Steve Howe -"The Clap"
Chet Atkins was right up there with Merle Travis - if we're defining a country style as well...
Let's move to the Blues: Freddie King -a plastic thumb pick and a metal index-finger pick helped to define a modern blues style of playing. Honorable Mention: Albert Collins who out and out just plucked with his thumb and fore-finger producing notes that would burn through your brain like lasers through styrofoam....
All of the above were trend setters with different styles that will help you to choose your own style...