I have posted a rather long overview of the most frequent Anti-Sicilan lines from the viewpoint of a Accelerated Dragon player in a forum thread and thought I might want to share it with you here in my blog as well:
I agree with LavaRook that you don't need to know too much theory to play the Open Sicilian at lower levels (<2000), as most Black players won't have all of their variations memorized either. Nonetheless, if you don't keep your theory strictly up to date, there is the possibility to be outprepared in tournaments where there is access to some of your games (databases, tournament bulletins and the like). To avoid this, a lot of players play the so-called Anti-Sicilian lines, which in most cases are not stronger than the Open Sicilian, but keep the first player on more familiar territory. Some of these Anti-Sicilians are hardly less challenging than the Open Sicilian itself, and therefore have acquired a lot of theory in their own right, others are just harmless or outright bad. I will deal with them in order of decreasing importance, keeping in mind that you usually try to reach the Accelerated Dragon.
- The Alapin (2.c3): The main moves here are 2...d5 and 2...Nf6, taking advatage of the fact that White doesn't have Nc3 at his disposal to defend e4. Sergey Tiviakov, specialist of the Alapin with both colours, claims that of these two possibilities 2...Nf6 is the only one to give Black hopes of equality in a complicated fight. So much for the viability of this particular Anti-Sicilian. Recently I have met an interesting system over the board quite often which might be interesting to you as a Acc.Dragon player: 2...g6 3.d4 cxd4 4.cxd4 d5 5.e5 Nc6 with the idea of Nh6-f5 in connection with h7-h5, securing the knight and putting pressure on d4, later on with Bg7 and f7-f6 as well. This scores quite well for Black, according to my database, but if White plays accurately, he should end up with the usual slight advantage.
- 1.e4 c5 2.Nf3 Nc6 3.Bb5, the Rossolimo has won quite a few famous games for White too, and thus is another Anti-Sicilian to be taken very seriously. The most fashionable answer for Black is 3...e6, while the older mainline 3...g6 is in some difficulties atm I think and 3...Nf6 is much better than its reputation. However, if you are willing to play the Hyperaccelerated Dragon (1.e4 c5 2.Nf3 g6) and the 2...g6 system against the Alapin, then you can skip the whole Rossolimo theory by playing 2...g6.
- Closed Sicilian (1.e4 c5 2.Nc3 Nc6 3.g3 g6): White's most usual plan is a pawn-storm on the kingside after having finished development. For that reason make sure you don't put your knight on f6, which facilitates the first player's aggression. Rather go for a setup with Bg7, d6, e6, Nge7 and 0-0. Your plans will include control of d4 (so White doesn't switch plans with d3-d4 at some point, although in certain cases even that doesn't have to worry you), queenside play by means of Rb8 and b5-b4, and, very importantly, stopping White's kingside play by f7-f5 at the right moment (usually after White has played both f4 and g3-g4).
- The King's Indian Attack, which starts with 1.e4 (or 1.Nf3) and the moves d2-d3, Nf3, Nbd2, g3 and Bg2. Your setup can be played quite alike to the Closed Sicilian: knights to c6 and e7, kingside fianchetto and pawns on d6 and e6.
- 1.e4 c5 2.g3 d5 3.exd5 Qxd5 4.Nf3 Bg4 5.Bg2 Qe6+ 6.Kf1 Nc6 looks daft, but isn't half as harmless as it seems - actually it has become quite a bit of a nuissance for Black. The arising positions are very complicated and original, and so this system can't be properly explained in a post like this. I just recommend to look up a few games with it and study them carefully.
- The Grand Prix Attack is an extremely successful attacking system, which despite having hunted down quite a few Grandmaster scalps is considered to be not quite correct. After 1.e4 c5 2.f4 you'd best follow up with 2...d5 3.exd5 Nf6, offering a gambit after 4.c4 e6. I should mention there is a delayed version of the GPA, which goes 1.e4 c5 2.Nc3 Nc6 3.f4 g6 and now either 4.Bb5 Nd4!, which is better now than after 1.e4 c5 2.Nf3 Nc6 3.Bb5 Nd4?!, because after the exchange on d4 Black wins time by attacking the c3 knight, or 4.Bc4 e6 5.Nf3 Bg7 6.f5 Nge7! with very sharp play.
- 2.b3 can be quite tricky to meet. Quite often it is recommended to play for 2...Nc6 3.Bb2 e5 4.Nf3 (the sharp 4...f4 is possible and should be studied accordingly) 4...d6, followed by g6, Bg7 and Nge7, trying to put a clamp on the d4 square. This is quite reliable, but I like to play 2...b6, followed by a setup in hedgehog manner: pawns on d6, e6 and a6, if necessary, bishops to b7 and e7, knights to f6 and (mostly) d7.
- The Smith-Morra Gambit has a lot of devotees, especially at sub-GM level, but most strong players will probably tell you that White doesn't get quite enough for the pawn. After 1.e4 c5 2.d4 cxd4 3.c3 dxc3 4.Nxc3 Nc6 5.Nf3 d6 6.Bc4 a6 7.Qe2 I like the system beginning with 7...Nf6 (make sure you play this before ...Bg4, otherwise you will fall for the trick Bxf7+ Kxf7 Ng5+, regaining the piece on g4) 8.0-0 (8.h3 is possible, but slows down White's attacking build-up) 8...Bg4, when Black solves the problem of his slightly cramped queenside and swaps off a potential attacking piece. Personally I have a very good score with this against the Morra Gambit, but if you don't feel like preparing for this gambit, you should be aware that by 2...d5 or 2...Nf6 or 2...g6 you can transpose to your favourite Alapin line, since White won't get around cxd4 for long. The benefit of this is that you have surely taken the Morra player out of his familiar environment, in trade for the obvious downside that you have forced him to play a system which is considered quite viable. Nonetheless there are situations where this may be appropriate.
- The Wing Gambit's reputation is even more dubious than the Smith-Morra's: 1.e4 c5 2.b4 cxb4 3.a3 should best be answered by 3...d5.
- 1.e4 c5 2.c4 aims for the so-called Botvinnik centre (c4-d3-e4 or c5-d6-e5 respectively). You can either do the same by 2...e5, followed by Nc6, d6, Nge7, g6 and Bg7, or you can try the following: 2...Nc6 3.Nc3 (3.Nf3 with d4 next will bring us back into the Maroczy bind against the Accelerated Dragon, which we should be happy to oblige) 3...g6 4.d3 Bg7 5.Nf3 d6 6.h3 (otherwise ...Bg4 becomes possible, which pronounces the weakness of the d4 square) 6...Nf6 7.Be2 Nd7!? 8.0-0 Nf8, transferring the knight to d4 via e6. I should mention that 5.g3 d6 6.Bg2 Nf6 7.Nge2 is possible as well, but you can play the same plan of transferring the knight quickly to d4. If White follows up with a quick f4 without having prepared this by h2-h3, make sure you play ...Bg4, again enhancing the d4 weakness.
- After 1.e4 c5 2.Bc4 we have already discussed that 2...e6 looks like the most natural move, but may transpose into a Sicilian main line you didn't want to play. Therefore I suggest 2...Nc6 and a further setup according to the Accelerated Dragon, where we will most likely transpose back to. Those cheapscates who really try for a scholar's mate by 3.Qf3? will find themselves bereft of the bishop pair after 3...Ne5, protecting f7 at the same time.
So, I think this is about it. Obviously it's impossible to discuss the Anti-Sicilians in any real depth here, so you should definitely use other media to deepen your study. You can either look up all these lines in a database (preferbly one which contains commented games as well), or you can buy a book on Anti-Sicilians, I think the most recent one has been written by Richard Palliser. Before him Dorian Rogozenko has written another volume on this topic, while the most instructive book has probably been Joe Gallagher's "Beating the Anti-Sicilians". It suggests systems which are not only playable but actually fun, but unfortunately it is quite dated by now (it's from the 1990ies) and also out of print.
Hope this helps in some way, and I'm looking forward to all those answers like "You are wrong, the *fill in name* is the best weapon ever against the Sicilian!"