Last year I did my grade 12 physics final project on this topic. To super-simplify it (ignoring center of gravity, wheel coefficient of friction in x and y, gear ratios, etc) the rule of thumb is that you want your wheel base to be at least as wide as it is long.
There are multiple ways that a 6wd, no-drop center drive train can be effectively executed. The two most popular as far as I know are the following:
Wide Base 6wd:
This drive base is exactly what you describe, only the drive base is in wide configuration. The reason this works is because as our rule of thumb dictates, the base is wider than it is long.
This is a kit of parts base, which does have a drop center, but it looks just like one would without the drop, just pretend
http://www.chiefdelphi.com/media/photos/37486
4 traction + 2 omni:
This drive train is probably more like you are envisioning, a standard long orientation, 6 wheel drive robot. The thing that allows this one to turn without issue is having omni wheels on one end. Omnis have very little friction sideways due to the rollers, essentially serving the same "cut the drive base in half" that a drop center does.
Something like this, except with omnis only at one end:
http://www.chiefdelphi.com/media/photos/31039