The Center Counter (1 e4 d5) is active and relatively easy to learn:
Icelandic Gambit: 1 e4 d5 2 ed Nf6 3 c4 e6 4 de Be6
Portugese Gambit: 1 e4 d5 2 ed Nf6 3 d4 Bg4
You can play the Tarrasch Defense (1...d5, 2...e6, 3...c5) against almost any White opening. Black usually gets an isolated d-pawn, but has active pieces as compensation.
As White:
King's Gambit: 1 e4 e5 2 f4
Alapin Gambit: 1 e4 e6 2 d4 d5 3 Be3 de 4 Nd2
Ulysses' Gambit: 1 e4 c6 2 d4 d5 3 Nf3 de 4 Ng5
Smith-Morra Gambit: 1 e4 c5 2 d4 cd 3 c3 dc 4 Nc3
Gambits are fun, albeit dangerous for both sides.