I will start by some gambits which are legitimate tries for advantage (for white) or for equality (for black) - so gambits which are not dubious as in they are as good as possible.
Most common example is Marshall attack in Ruy lopez, which is today studied so well it's practically book draw. White players commonly today play anti-marshall lines to dodge it.
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[Startply "16"]
1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. O-O Be7 6. Re1 b5 7. Bb3 O-O 8. c3 d5
In Semi-Slav complex there are two very respected gambits. First of them is Anti-Moscow gambit, which leads to very irrational positions:
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[Startply "14"]
1. d4 Nf6 2. c4 e6 3. Nf3 d5 4. Nc3 c6 5. Bg5 h6 6. Bh4 dxc4 7. e4 g5
And Marshall gambit:
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[Startply "11"]
1.d4 d5 2.c4 e6 3.Nc3 c6 4.e4 dxe4 5.Nxe4 Bb4+ 6.Bd2
English and Benoni (due to transposition) players will be familiar with Kasparov gambit:
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[Startply "12"]
1. d4 Nf6 2. c4 c5 3. Nf3 cxd4 4. Nxd4 e5 5. Nb5 d5 6. cxd5 Bc5
In this line of Phillidor Shirov gambit is probably most critical. Position can also be reached through Pirc move order:
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[Startply "9"]
1. e4 e5 2. Nf3 d6 3. d4 Nd7 4. Nc3 Ngf6 5. g4
Lets switch to gambits which promise white "merely" equality in case of black best play - so gambits which are not dubious as in they do not lead to worse position.
Most promising of these probably is Urosov gambit, even though it is old enough to be considered romantic. Most lines in it promise white at least some advantage, except 4. ... Bb4+, which tends to lead to equalish endgames. Black can easily dodge it though by transposing to open variations of two knights defence.
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[Startply "9"]
1. e4 e5 2. Bc4 Nf6 3. d4 exd4 4. Nf3 Nxe4 5. Qxd4
Evans gambit also promises at least equality for white in all lines. However black has available plenty sound defences to choose from.
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[Startply "7"]
1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. b4
Staying in Italian complex I believe that good old Møller attack is still considered book draw:
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[Startply "17"]
1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. c3 Nf6 5. d4 exd4 6. cxd4 Bb4+ 7. Nc3 Nxe4 8. O-O Bxc3 9. d5