My brother used to ride like that, as did a few other people I knew.
Popping the shields off can make the bearings run faster because without the seals you have less friction. Also, all the lubricant will probably come out and they'll get a lot louder too. The ride is much less smooth also. Other downsides are that you're exposing the cages and balls to the elements, which means they'll get dirty and the bearings will wear out a lot faster. I'd imagine that you have a much higher likelihood of breaking a bearing with the seals popped off.
Personally I'd rather have a decent set of bearings that I take care of and replace when necessary than ride around on ones with popped shields, but that's just me.