As White, I stick to normal stuff. The typical e4 is where I like to go. If I do a d4 opening, it's usually the Queen's Gambit. I also like to do the Reti or KIA occasionally, as well as the Scotch (e4 e5 / Nf3 Nc6 / d4) and Ponziani (same as Scotch, but with c3 instead of d4).
As Black, my usual response to e4 is either the Sicilian or Caro-Kann. For d4 I usually just go d5, rarely using the KID and occasionally using the Slav (same as the Caro-Kann, only it's played in response to the Queen's Gambit). If I do d5, I like to do the Krause (2. c5; basically the Queen's Gambit for Black) if White's second move of choice is Nf3.
Rarely, people will do 1. c4 as White. This isn't bad, but most people will tell you not to play it as it can be very tricky to play well. If you're Black, the best response to this is probably 1. e5.
I'm learning the Sicilian Defense, but I don't know what to do if White doesn't play e4 . Recommend a few openings for both White and Black, not too many—just enough to handle most positions.