Hmm, let's see, the most effective two-type attack combos(keep in mind Shedinja, thanks to Wonder Guard, is neglected, as it should be obvious only SE attacks hurt it):
Bug/Rock: Resisted by most fighting types, ground or rock/steels, ground/poisons, and that's about it. EQ rounds out the coverage easily. Seen on Armaldo, Pinsir, and Heracross.
Dark/Fighting: Only resisted by Toxicroak and Heracross(IIrc). Seen on TyraniBoah and Darkrai. A fire move rounds out coverage.
Dragon/Fighting: No resistance. Seen on CB/Mix Dragonite.
Dragon/Fire: Unresisted type-wise. Heatran resists(and Bronzong if Heat Proof), due to Flash Fire. Seen commonly on just about every dragon that can get its hands on it, as well as on Heatran(Dragon Pulse). A ground move rounds out coverage.
Dragon/Ground: Only Skarmory resists type-wise, with Bronzong if it has Levitate. Seen commonly on Garchomp and Flygon, although every physical dragon typically packs the combo. A fire move rounds out coverage.
Dragon/Water: Only Empoleon resists. Commonly seen on Kingdra, but also Latias(Surf). CBers like Salamence and Dragonite also use it(Aqua Tail). An electric, fighting, or ground move rounds out coverage.
Electric/Ice: Only Magnezone and Lanturn resist(IIrc). Commonly seen with electric types, with HP Ice, Ice Punch, or Ice Beam. A fighting or ground move rounds out coverage.
Fighting/Ghost: Unresisted. Seen on Gengar.
Fighting/Rock: Only ground or fighting/poison types resist. Commonly seen on Toxicroak to provide additional coverage, as well as Hariyama and sometimes Lucario. A ground or ice move rounds out coverage.
Flying/Fighting: Only resisted by Rotom and Zapdos. Commonly seen on Staraptor and Honchkrow. An ice move rounds out coverage(or for the examples above, a dark/normal).
Electric/Fire: Only resisted by Lanturn(ability), some dragons, and ground/waters. Commonly used by Zapdos(Heat Wave). HP Ice/Grass rounds out coverage.
Ground/Ice: Only resisted by Bronzong(Levitate). Commonly seen on Mamoswine. A fighting or fire move rounds out coverage.
Normal/Water: Only resisted by Empoleon. Commonly seen on Gyarados or Kingdra(to provide coverage without drawbacks of Outrage). A ground, electric, or fighting move rounds out coverage.
Water/Rock: Only resisted by Toxicroak(Dry Skin), Empoleon, Quagsire(Water Absorb), and Breloom. Seen on Rhyperior, Relicanth, and Aggron. Can be rounded out by a fire or ground move.
I might have forgotten some combinations/resists, but for the most part, these are the most important. The "rounded out by x move" section aren't the only possibilities, but typically the most effective in terms of coverage.
Seeing this list, I'm sure dragon is the best attacking type. Move away from its typically amazing BST pokemon and movepools/moves(Outrage/Draco Meteor), but it also can easily be paired with other types of moves for great coverage. On top of this, many dragons have access to atleast one of those types of moves, furthering the types dominance.