Third-move anti-Gruenfelds
After 1. d4 Nf6 2. c4 g6, the most popular non-Nc3 moves are Nf3, g3 and f3.
As you already know,
3. Nf3 renders the immediate 3... d5 really bad - after 4. cxd5 Nxd5 5. e4, there's no knight on c3 for the taking, so Black has to retreat the knight to f6 (which is a bit better than b6), and then White typically develops the LSB to c4 or e2 (or to b5 after Nb6), poised to convert the development advantage into an attack.
However, Black can do quite well by delaying d5 (moving Bg7 and O-O first) until one of the two things happens: 1) White develops the other knight to c3 (enabling Nf6xd5xc3), 2) White develops the LSB to g2 (in this case, after Nf6xd5-b6, Black is in no big trouble because White's LSB is not targeting the kingside).
That's of course applicable if Black isn't willing to play KID, which is quite good itself.
Vs 3. g3, the best option imo is the Catalan transposition - 3... c6 and 4... d5 (if cxd5, then cxd5, otherwise Black can play dxc4 and feel good because the g2 bishop is blunted by the c6 pawn).
3... d5 is playable, but note that the best response to 4. cxd5 is a gambit (a computer line that, amazingly, has never been played in games covered by free databases) - 4... c6! 5. dxc6?! Nxc6 6. Nf3 e5 7. dxe5?! Qxd1+ 8. Kxd1 Ng4 9. Ke1 Bc5 10. e3 Be6 11. b3 Ncxe5 12. Nxe5 Nxe5 13. Bb2 Bb4+ 14. Bc3 [forced, otherwise Black develops a big attack, e.g. Kd1 Bg4+] Bxc3+ 15. Nxc3 Rc8 and so on - Black is a pawn down but has the initiative.
The problem with 3... d5 4. cxd5 Nxd5 is that, after 5. e4 Nb6, White can develop the knight to e2, leaving the fianchettoed bishop more active, as opposed to the 3. Nf3 line, and then plays d5.
Vs 3. f3, as I've already said
here, good responses are Bg7 followed by d6 (KID), c5 (the Modern Benoni) and e5 (the Leko Gambit), though I find 3. f3 the best anti-Gruenfeld out there. Which one to choose is again a matter of personal preference and familiarity with the Benoni and KID.
I hope you've understood the reasoning behind my rants, I'm sorry for their verbosity.