I like collecting coins as much as the next person, but what can I use them for in Mario Kart 7? Do I get a free life if I collect enough of them?
Unlike in the first Mario Kart, where they acted as a buffer against other players crashing into you, coins appear to act as currency now for buying new kart components.
Source: Mario Wiki
When you run over a coin, you get a short burst of extra speed. Each coin that you get in a race, up to 10, will increase your Kart's maximum speed.
Your cumulative total of coins collected will unlock options for your Kart - including alternate Kart bodies, wheels, and gliders.
Coins will not grant a free life.