This desire for the quick, gimmicky wins goes back, for most of us, to our early experiences with the Scholar's Mate (1.e4 followed by 2.Bc4, 3.Qh5 and, if all goes well, 4.Qxf7#), but the world of junior and beginning chess is rife with this sort of thing.
One such line goes as follows: 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nd4?!, when Black's big idea is to sucker White into capturing the "free pawn": 4.Nxe5 Qg5 5.Nxf7 (more freebies?) Qxg2 6.Rf1 Qxe4+ 7.Be2 Nf3# (perhaps it wasn't so free after all).
White can achieve an easy edge with moves like 4.c3 or 4.Nxd4, but neither move really punishes Black in the way he or she so richly deserves! Black wants to destroy White by giving up some material in return for an attack; I say we return the favor. Two lines come to mind:
(a) 4.Nxe5 ("falling for it") Qg5 5.Bxf7+ Ke7 6.O-O Qxe5 7.Bxg8 Rxg8 8.c3 followed by 9.d4. White has two pawns, a massive presence in the center and an exposed Black king as compensation for the piece. Objectively, the position may be roughly equal, but as a practical matter White's position is much easier to play.
(b) 4.Bxf7+ Kxf7 5.Nxe5+ Ke7 (the brave 5...Ke6 is interesting, but 5...Ke8 6.Qh5+ should win for White) 6.c3 d6! 7.Nc4 Nc6 8.d4 Nf6 9.O-O Kf7. Here White probably lacks sufficient compensation, though I think practicing such a position in blitz and casual games is both educationally worthwhile and likely to result in a reasonable rate of success.
Objectively, the normal lines are best, but lines (a) and (b) are more fun and, in a certain way, more appropriate responses to 3...Nd4. Speaking generally, one should try to achieve two things in the opening, when possible: reach a type of position one finds comfortable and, when possible, that one's opponent does not. These lines do just that.