I'm using New Balance Minimus almost exclusively, and my other shoes are Innov8 somethingorother trail shoes with a 0mm drop.
The main reason for looking for these shoes was because I wanted to try running without a heel, to allow my tendons and muscles to act as shock absorbers. The theory (in my head) being that the could give me back some of the energy absorbed from my landing, instead of having it dissipated in cushioning.
Not sure if that's worked, but now I run nicely on my mid or forefoot and I'm happy. On the upside the NBs are very light, all other shoes seem like weights now. Downsides for those particular shoes are that there are no insoles so I get the odd blister now and then if I don't use cushy enough socks.
Using the flat shoes has really helped my form I think. I'm far lighter on my feet and I can really feel my feet working and moving, which is a nice feeling. Cushioned shoes now feel like trying to play the piano in boxing gloves.
Normal cushioned heeled shoes feel awful now, can't stand to run in them.
EDIT this is all on road btw.