Anyone know what this opening is called? I usually grab the Gambit pawn by exd4. The ensuing game consists of me defending for quite a while. Thanks!

You mean the following I presume?
1. e4 e5 2. d4


It's the Center Game. It can transpose into a number of other openings (Scotch Game, Danish Gambit etc) but has its unique lines following
2. ... exd4 3. Qxd4.

Assuming you mean the Center Game, the best option (by far) is to take the d-pawn. Alternatively, there is a line of the Nimzowitsch defense (that I wouldn't recommend following 2. ... Nc6.
The Center Game is okay for getting a quicky by means of surprise. Typically white will get an equal game going (a Scandinavian reversed) but nothing more.

1. e4 e5 2. d4 exd4 3. Qxd4 Nc6
They go Qc4 (not a good spot for the queen in any opening I know), or Qe3 (the main choice) or Qa4 (a proper Scandinavian reversed). The problem with the Center Game is that the queen shouldn't be out there. Black can develop around it, play d5 and be equal. There are some annoying rook sacs and maneuvers out there. Ever seen a rook on b5 (covered by a Nc3) attacking a queen on b6 right out of the opening? It's actually a plan that recurred in several games I've played...

As for the transpositions I mentioned. The Danish, half-Danish, Goring, nobody plays those with any enthusiasm anymore. There is a Petrov line (Steinitz variation) to avoid the Scotch 1. e4 e5 2. d4 exd4 3. Nf3 Nf6; but I prefer playing 3. ... Nc6 4. ... Nf6 (Schmidt variation Scotch).

D5 is a typo.. I meant what you said D4. Thanks for the info I will look it up.

Well, I don't think I really need to make another post for this, so what is 1. e4 e5 2. Nf3 d5 called?

Queen's Pawn Countergambit. May lead to the Elephant Gambit after 3. exd5 Bd6 (some of my sources say 1. e4 e5 2. Nf3 d5 is the EG, but I don't think so). Falls in the same category as the Center Game for white if you ask me. You can get away with it, but it's really not a very good defense.

Oh okay thanks. I have no intention of playing it, I just wanted to know because one of my friends played it against me earlier and I was confused. I didn't think something like that would have a name. I just decided to take the d-pawn. Is that what white is supposed to do?

Supposed to do? Well, 3. Nxe5 is just as playable, though it (if I recall correctly) has a tendency to end up in somewhat (or a lot) more tactical positions. 3. exd5 is a perfectly good 'safe' way to go. It's a bit of a trick opening, in double e-pawn openings, black (and white) strive to advance the d-pawn 2 squares up without penalty. If the QPCG worked the way it should, masters would play it on principle. They don't because the opening has some annoying flaws.

isn't it the Danish Gambit?

No. The Danish Gambit is as follows:
1. e4 e5 2. d4 exd4 3. c3
In so doing offering a pawn (or sometimes two) for development.

Ah okay, thanks once more.