There are 16 brand new tracks, same as in every other Mario Kart game.
There are also 16 tracks from the previous four games, four each from each version. I'll go ahead and list them. From:
SNES - Mario Circuit 1, Donut Plains 1, Koopa Beach 2, Choco Island 2
N64 - Moo Moo Farm, Frappe Snowland, Choco Mountain, Banshee Boardwalk
GBA - Peach Circuit, Bowser Castle 2, Luigi Circuit, Sky Garden
GCN - Luigi Circuit, Baby Park, Mushroom Bridge, Yoshi Circuit
As far as characters, there are 12 characters, though only 8 are initially available. The initial 8 are Mario, Luigi, Peach, Toad, Yoshi, DK, Bowser, and Wario. The four unlockables are Dry Bones, Daisy, Waluigi, and R.O.B.
Initially only 2 karts are selectable for each character. Earning gold on every race in the Nitro Cup on 100cc will unlock a third kart for each character. Getting gold on every race in the Nitro Cup on 150cc will unlock 7 (!) karts for each character. And finally, getting gold on every race in Retro Cup on 150cc will allow you to choose any character's kart for any other character (imagine Bowser racing in one of Toad's karts!).