In quick games lots of lower rated plays try scholars mate as white and play 1.e4 2.Bc4 3.Qf3 against everything. 2.e6 is solid followed by nf6 a6 b5 with tempo on bishop then get castled and attack on queen side and you should fine.
Sicilian 2.Bc4
It's common at all time controls. They're usually 1...e5 players themselves who wish you'd played 1...e5 against them and they wish it so bad they decide to pretend that's what happened and try to play an Italian Game against you anyway. What's worse is if you play a d6 Sicilian, if they go 2.Nf3 d6 then Bc4 the plan with e6-d5 has lost a tempo.
Against the immediate 2.Bc4 I prefer now 2...Nc6 first before e6, because I'd prefer to develop a piece rather than make a pawn move there, also they're more used to seeing 2...e6 so 2...Nc6 perhaps makes them feel a tad uneasy, e6 will be played soon enough. After 2....Nc6 White should bring out one of their knights to which Black should play 3...Nf6. After this e6 usually follows. Against an e5 push d5 is usually the answer.
In many variations after e6-d5 the e-file opens and the pawn structure is similar to the French Exchange. After e6-d5 if the bishop goes to b5 pinning the knight a policy decision must be made whether you want to allow the doubling of your c-pawns in exchange for the bishop pair or if you'll play Bd7 or something. Practically lI think Bd7 may be the better thing to do.
Also sometimes they'll play a quick a3 or a4 to tuck the bishop back on a2. In these variations I've sometimes been able to trap the bishop there, even once entering a light square vs light square bishop ending where their bishop was on a2 with a black pawn chain a6-b5-c4 and my bishop controlled the h7-b1 diagonal so there was no way for them to get it out. It's kind of hard to achieve this but when you're able to it's absolutely great.
The White player usually tries to be aggressive and shunt all their pieces over to the kingside. I think for this reason making the e6-d5 break early is a good thing to do, after an exchange on d5 with the e-file opening all the heavy pieces tend to get exchanged and the game becomes like a French Exchange but my king seems to come under less pressure there.

Yes, very interesting. I hadn't considered that they were just sticking rigidly with their Italian Game type gameplan come what may! I suppose they just hate the Sicilian and try and force you into an Italian game, but like others have said, when defended properly, it just loses tempo for white. I'll have to make sure I don't panic against it in future, because it strikes me as a terrible opening against the Sicilian. I'm not sure it even has a name!
And thanks for the suggestion against the e5 push Dolphin! That's often been my weakness when I get into this situation.

well yeah your opponent played an inferior move against your sicilian. However do not try punish him immidiately (by going for quick ..e6-d5 to gain tempo on the bishop) because it backfires. Instead be patient, and keep flexibility (don't castle yet, keep the pawns on c5,d6,e6). White will eventually have to either play d4, when it will transpose to a sozin sicilian or start a kingside attack even though you haven't commited with the King yet.
Well, it's not quite a terrible opening it just gives Black equality. One of the things I've seen written in an anti-Sicilian book is that a theme amongst all the anti-Sicilians is that they're underestimated and we as Black shouldn't fall into the mental trap that our opponent has done something wrong.
In the lines where White has played e5 and Black has played d5, it can end up like exNf6 dxBc4 fxg7 Bxg7 When Black's pawn structure is a little messed up but he's gained the bishop pair. I've not actually had that variation happen often in my games.
For a while I was playing a set-up where I omitted the d5 push and just put my pawns on e6, d6, a6, and b5, and my light square bishop on b7. What would invariably happen in these games is White would start shunting all their pieces over to the kingside (manuevering thier knights as if in an Italian game) they would move their queen out to the kingside as well and start pushing their f-pawn at some point hoping to often the f-file for the rook on f1 and bishop on the a2-g8 diagonal. While they were doing this I would centralize my heavy pieces and only then try to make a pawn break in the center. Those games were more exciting than all the games where I made the e6-d5 push early, often causing an exchange on d5 and creating the French Exchange structure, but my king definitely came under more fire.
I think that since someone has had the rudeness of copy and pasting a post made here without attributing it to its writer that this thread deserves a bump so it can be seen in the right context.
When I play the Sicilian defense in 10 minute blitz matches, I'm always amazed at how many people play 2.Bc4. As far as I can tell, this is a very obscure variation. Why is it so popular at lower levels? Annoyingly I do really badly against it. I think I need to play 2...e6 next rather than bringing my knights out first.