I've never had a taste for theoretical lines where you gambit a pawn for dubious compensation e.g. the Budapest, the Scotch Gambit or the King's Gambit. That's just me personally. You have to really know what you're doing.
That includes the line of the Two Knights Italian where you avoid the Fried Liver Attack.
Halloween gambit, Muzio Gambit (I always avoid it by playing the less risky ...Bg7 and white gets no compensation for the pawn), Fried Liver Attack, Lolli Attack, Sicilian Dragon (as black, I fear it, as white, I love it).
The Latvian gambit always has some tricks because I don't know which pawn to take and I've had much trouble facing it as white
Are there any simple gambits to play as white for the d4 player? (Not Queen's Gambit obviously)
@HydroMask Against the Latvian Gambit, there is a relatively simple line which does not seem to require much theory or memorization and gives White a good game in my opinion: 3.Bc4.
See for instance: lichess.org/cjzW187g/white#5
Please don't be bothered by the result of the game (Black won); if you look at the computer analysis you'll see that White had great advantage during the middle game. The loss was not a result of the opening.
@hampy It would feel wrong for me to refer to the BDG (Blackmar-Diemer Gambit) as simple, but it sure can lead to interesting play and is probably a lot better than its reputation. 1.d4 d5 2.e4 dxe4 3.Nc3 Nf6 4.f3 exf3 5.Nxf3
5.Qxf3 instead is the Ryder Gambit with the ever popular Halosar trap (see for instance www.youtube.com/watch?v=6Vhu9qDkkws) and also worth exploring, but the normal BDG with 5.Nxf3 is better in my opinion.
@hampy : Why not the queen's gambit? The Albin Countergambit (1.d4 d5 2. c4 e5!?) is quite exciting!
ahh.. this is easy: most defintly the bongcloud
@clousems The QG isn't considered to be a true gambit as far as I know. Your suggestion, although appreciated, is a gambit for black isn't it?
I'm after something for white after 1. d4...
@hampy : short answer: yes. The Blackmar Diemar gambit in d4 d5 openings is unsound but playable. But if you are a gambit player, why are you playing d4 openings?