Is there a list of part 121 and/or 135 operators?
I have not found a list, but you can search for an airline here.

There is a link on the page to definitions of the terms. Basically, "domestic" and "flag" are FAR 121 operations, and "commuter" is FAR 135 operations.

There is also an unofficial database here that will tell you which FAR an airline operates under.