Some gambits are playable whether the gambit is accepted or not, such as the Queen's Gambit, the King's Gambit, the Evans Gambit and the Budapest Gambit. Some are just dubious (the Elephant and a host of others). Some are playable if they're accepted, but the Declined forms are just worse for the gambiteer. Which gambits fall into this category?
One example is the so-called Calabrian Countergambit: 1.e4 e5 2.Bc4 f5. After 3.exf5 Nf6, black seems to be fine. However, white should ignore the gambit and play a developing move: 3.d4 (Bologan-Bednarek), 3.d3, 3.Nf3 or 3.Nc3.
[StartPly "4"] [FEN ""] 1.e4 e5 2.Bc4 f5 3.exf5 (3.d4)(3.d3)(3.Nf3)(3.Nc3) Nf6
Another example is a line in the exchange variation of the Ruy Lopez: 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Bxc6 dxc6 5.0-0 Bg4 6.h3 h5. Accepting the sacrifice with 7.hxg4 is clearly too dangerous as it opens the h-file for the black rook. White is probably slightly better if he declines the sacrifice with 7.d3 (Naiditsch-Mons).
[StartPly "12"] [FEN ""] 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Bxc6 dxc6 5.O-O Bg4 6.h3 h5 7.hxg4 (7.d3) hxg4
In the Blackburne Shilling Gambit
1.e4 e5 2.Nf3 Nc6 3.Bc4 Nd4,
[StartPly "6"] [FEN ""] 1. e4 e5 2. Nf3 Nc6 3. Bc4 Nd4 4. Nxd4 (4. O-O) (4. Nxe5 Qg5!)
black gambits the
e5-pawn, but white gets an advantage if they simply decline the gambit with
4. Nxd4 or
4. 0-0. Black is behind in development.
If white accepts the sacrifice (
4. Nxe5), then black gets good play with