as white 1.e4 and gambit like crazy - smith-morra, KG; with black play against 1.e4 Sicilian or Scandinavian and against 1.d4 Budapest, Dutch or KID. I use these and although have many losses I also have many nice wins. Most importantly - I enjoy chess :)
Good openings for unbalanced positions?

dont worry about the openings making you aggressive.
I play some of the most 'drawish' openings around, and I only draw about 20% of my games because I often play quite aggressively, only against higher opposition do i content to the drawish nature of the position.

By simply playing the main lines, you will find that white fights for advantage in all lines. Or at least tries to make it complicated. Quality Chess says: ¨Tired of bad positions? Try the main lines!¨

By simply playing the main lines, you will find that white fights for advantage in all lines. Or at least tries to make it complicated. Quality Chess says: ¨Tired of bad positions? Try the main lines!¨
Second the motion! BUT to fill in a few blanks:
vs 1.e4 avoid the Petroff Defense and CaroKann Defense. If you play 1.e4 as White forget about all the Double KP Openings vs. 1...e5 except for the RL (and maybe KG if you're a real swashbuckler) Statistically the IG still looks like a valid winning try for White but I'd go with the RL myself.
As White avoid almost all "Exchange Variations" except for the QGD Exchange Var which can make Black miserable for a long time in some cases
vs 1.d4 the Budapest is an aggressive reply and just as good as anything more "solid" or "mainstream" esp OTB for most of us amateurs; or you could try the Albin Counter-Gambit or Tchigorins Defense if you're brave enuff. Otherwise there's always the KID or Benoni if you can avoid getting squeezed off the bd by White in those lines.
I'm a bit tired of getting into drawish positions, which led to trading a lot of material and reaching even more drawish endgames. What openings do you know that give both sides good chances and have the lowest draw rate?