Edit: I took a look at the related question. The first answer illuminated me to free form ABCD... (let's not forget about free form!) and a good structure definition of Sonata. The other answers apparently did not have any ABC lettering description of forms (maybe I'm using a strict definition of "form"?). In any case, my question remains if any more basic forms exist (are well-established in baroque/classical/early romantic periods). I edited the title to include the word basic.
I only know 5 official forms:
ABCD... for Free Form
AA'A'' for Variations on a theme
ABA for the Minuet and Trio
ABACA for the Rondo (sometimes called ABA'B'A'')
ABABC(AB)' for Sonata
Surely there must be more? I could make up something like ABBA or any random combination of letters but I'd rather investigate the official forms first.
I wrote a Rondo and M&T years ago for the piano. I've wrote variations on a theme for a long time (they seem to be the easiest). Now I'm looking for other forms to try my hand, or I'll just make one up and consider it an exercise.
I'm partial to piano music, but official forms that are traditional for other types are okay too.
Edit: The baroque, classical, and early romantic periods are very long times with many, many works. I would be very surprised if only 5 basic forms existed there.