I don't know that I qualify as a better player but my thoughts, for what they're worth:
Take the second approach ( 2. ... Nc6) and follow 3. Bc4 with 3. ... g6, followed by Nf6, Bg7, O-O. Simple, calm development and take advantage of white's wasted tempi in the queen follies.
Also, try looking at Learn menu and go to Book Openings. You can enter the opening and see the variations. E.g. http://www.chess.com/explorer/index.html?id=10580&ply=5&black=0
NickYoung5 is correct, Nc6 followed by g6 is the best way to play against this.
I don't think there is any outright refutation but black should obviously enjoy a more comfortable game than usual.
In the first example instead of 3... Qe7? try 3... Be7 - when you are a pawn down usually the last thing you want is to exchange queens. You'll have compensation in the form of your superior development since white'll need soon move the queen again.
In the second example as already pointed out by others, instead of 3... Qf6?! (bringing out the queen perhaps bit prematurely and taking out the most natural square from the knight) more natural is 3... g6 4. Qf3 Nf6 5. Qb3? (5. Ne2 is better) Nd4!.
The queen is on Nf6 :)
Thank you though. Some degenerate part of my brain was still convinced that g3 lost a rook but of course now that the queen is on Nf6 that isn't the case. In fact it looks to me like white is in a lot of trouble, as there's no good place for his Queen to go after 4... g3.
Both Qg4 and Qh3 are blunders which allow me to play d5, winning a piece. That only leaves my opponent Qh4 and in that position exchanging Queens looks positionally very advantageous. He must recapture with his knight, which goes to an awkward square and will cost him yet another tempo to defend after Be7. Both sides castle and the final position looks good for black, ahead in development and with a decent initiative to start building an attack.
Thank you very much, you have given me a nice answer to an irritating problem!
doh I see now you were talking about 3...g3 instead of 3... Qf3, not 4... g3
Oops that will teach me to read numbers better! :)
Qe7 isn't the book move, I think. Be7 is, and it's a gambit that gives Black good play since the White queen gets kicked around after Nc6, and Black has three pieces developed for the pawn. I haven't played against the Parham Attack too often, though! Played it once myself and was lucky to escape with a draw.
So it's called the Parham attack. Well its good to have a name for my nemesis :)
I suspect I see it a lot because of my low level. I'm keen to improve my chess and have numerous problems so I won't hijack this thread with my laundry list of questions, but expect more threads from me soon 
wow thank you so much guys... definitely some lines worth learning there. It seems a shame that no-one has outright bust the opening as it really looks like it should pay a stiff penalty for disregarding opening theory so blatantly.
@ManicMinerUK: That's the beauty of unorthodox openings. The psychological effect ("oh, that's a bad opening. I can win easily") combined with the fact that it's not immediately losing is sometimes enough to win games, so be careful when playing against seemingly unsound openings. They're not sound and might be -0.50 to -1.00 positionally, but remember that such an advantage is not necessarily decisive unless you play good chess.
Don't feel too bad -- Nakamura has played this goofy Qh5 line from time to time, even in some relatively serious games, and has done all right with it. It's certainly not what one would call a good opening, in that White is wasting his first-move advantage, but by no means does it create an immediately won or lost game for either side.
Play 1. ...c6
edited
I actually wasn't joking, but was tired and wrote c4 when I meant c6. I don't like 1. ...e5 because it is risky as demonstrated above. The best response is probably the sicilian but that involves a lot of theory. I think 1. ...c6 is a better move for me, because it is a safer move that does not require a bunch of theory to follow it up.
wow thank you so much guys... definitely some lines worth learning there. It seems a shame that no-one has outright bust the opening as it really looks like it should pay a stiff penalty for disregarding opening theory so blatantly.
For White to give Black equality in -- what is it 4? -- simple moves is a stiff penalty. You seem to think White's "violation of principle" constitutes a terrible blunder that should cost him the game... chess isn't quite that hair-triggered... basically he's misplaced a piece and that costs him tempo. If he continues throwing away tempi in the opening (as a beginner might, by continuing with futile queen attacks that are repulsed with developing moves) he'll soon be in really hot-water... but one lost tempo doesn't cost the game, or Black would be lost from the start.
Since specific lines have been posted already, let me give you a more general chess advice. Don't think so dogmatically. Just because an opening looks weird it doesn't mean you're winning on move 5. It's a very common mistake to overpress against an opponent that plays a dodgy opening only to find out you've gone too far and he/she is actually winning because of your reckless play.
Just try to play purposful moves. Don't get caught up in generic stuff, try to make a plan as early as possible and follow it or change it if it's neccesary to do so. Playing "normal" moves is something that should be avoided at all costs. Avoid routine-thinking and try to stay alert.
Actually, 1.e4 e5 2.Bc4 isn't bad at all, as long as you're not doing it with the intentions of Qh5/Qf3 for a quick mate on someone bad. It's quite transpositional, with the most common move being 2...Nf6, to which I reply with 3.d3 or 3.Nc3, planning some play on the Kingside with f4, Nf3, 0-0-0, Bd2/e3, etc.
Hi,
I'm hoping to get some advice of how to play against this opening. I've seen it a lot and it looks extremely suspect to me but I can't seem to find the outright refutation that is almost certainly deserves.
The following two games give a flavour of the paths my games tend to tread.
I should admit that this opening strategy irritates me greatly, as it violates most opening principles. I'd be interested to know how the better players on here would deal with it?