A Couple of Repertoire Suggestions

As Black:
Here are some recommendations for players who want to play less conventional openings with the black pieces. Both the Alekhine defence and the English defence are suited to quirky players who perform well under pressure.

1.e4 Nf6,

Alekhine's defence
Sharp, clean, little known. What more could you want?

1. e4 Nf6, 2. e5 Nd5, 3. d4 d6!, 4. c4 Nb6, 5. ed cd,+=

The position is unbalanced by the asymmetrical pawn structure. Black will try for pressure with rooks on the c file or possibly a kingside fianchetto. Central pawn advances are probably taboo.

1.c4 b6,

The English defence
Little known. Good chances for opening traps! May appeal to the tactically minded player (!)

1. c4 b6, 2. d4 e6, 3. e4 Bb7, 4. Bd3 Nc6, 5. Ne2 Nb4, 6. O-O NxB, 7. QxB Ne7+=

I'm not going to show you the position because you wouldn't like it! It's not really that bad ... just a little passive. GMs have played this position as black ... honest! ... Miles, Plaskett, Pshakis Kengis, etc. If you don't like it then just play the Nimzo! Alternatively you might try the slightly wet but playable move order 1. c4 e6, 2. d4 Bb4+ and only then play a queenside fianchetto. You do run the risk of transposing into a real opening but you will end up with a better position than you would have got with the English Defence!

If one were so inclined one could play the English defence against 1. d4 aswell ... :) Just make sure you don't play b6 untill white has played c4! Also, bear in mind that black often gets good tactical chances with f5 but watch out for checks on h5!