1) Geetham & Nottuswaram (department of redundancy department

2) Raga alapana
3) Tanam
4) Keerthana -- quite a bit of overlap with krithi
5) Krithi -- which covers everything in the spectrum
6) Padam
7) Javali
8) Thillana
9) Bhajans
10) Abhangs
11) Slokas, Ugabhogas, Viruththams, Pasurams
12) Neraval
13) Kalpanaswaras
14) Tani avartanam
15) Varnam
16) Harikatha
17) Jathiswaram
18) Pallavis - the RTPs I mean
19) Konnakol
20) Tiruppugazh
21) Pasurams (sung in talas), Thiruppavai, Thirvempavai, Tevarams, etc. etc.
22) Mallari
23) Ragamalikas & Talamalikas - which can fit into the above list, but I separated them out.
24) Ashtapadis
25) Nama Sankirtanam
26) Kavadi Chindu and folk items -- not too familiar here, would like a list.
27) Patriotic Numbers
28) The basic exercises - saralis, jantas, dhatus, alankarams, can't forget to include it. I mean there is almost nothing harder than a 4 octave scale in a raga with all the gamakas in Carnatic Music, is there?

Not to mention a lot of extinct musical forms... Did I forget anything?
One thing you notice here that over the course of CM history, that out of the elements mentioned above, you have a lot of these forms which were part of the musical system from the very beginning (or almost), whereas the others either got imported over time from other art forms or existed independently, started using CM and got absorbed into it.
In the future, there may even be new forms like Carnatic concertos and the like ... the vadya vrinda for one already exists. Who knows?
Any more forms out there (even extinct ones) would be a most welcome addition to the list