Honda will be putting ultracapacitors in their cars in the next few years. They will use it on a fuel cell vehicle to handle demand peaks.

Capacitors have some advantages and disadvantages relative to batteries.

The pluses: hey don’t wear out, and they can put out a lot of juice in a short time (they are in camera flashes).

The minuses: They slowly^* leak stored energy over time., and they have lower energy density.

The technology is advancing rather quickly^†, so the disadvantages may decrease.

You could also use the capacitors in conjunction with batteries to go with a higher energy/lower power battere (higher power means lower energy and vice verse),

^*Very slowly, as anyone who has gotten knocked on their when they open up a TV that has been in a junkyard for two years can attest.
^†When I was in school, I was told that a 1 Farad capacitor would be the bigger than a a pick up truck, now there are commercially available ones that are smaller than a thimble.