When I went full-boil with my extract brews, I purchased a larger pot (8.5 gallon) and moved the operation outside to a propane burner (like used for a turkey fryer). At first; I tried to boil what would've been a full volume for a 5 gallon extract brew - about 6.5 gallons - in the kitchen and even though I've got one burner on my gas range that'll go 18,000 BTU, it still was barely enough to get that volume to a simmer.
The boil should be vigorous enough to drive off the things you don't want in the brew like Dimethyl Sulfide (DMS). For this reason, you don't want the lid on during the boil. A vigorous boil is also needed to achieve a good hot break which is the coagulation of proteins that will settle out in the fermenter as trub, thus resulting in clearer beer. A vigorous boil will also improve hop utilization.
Being able to maintain a vigorous boil will improve your brew, but how vigorous? I generally go for a level of activity in the pot that looks like the surface is rolling fairly well, bouncing around, but not bouncing all the way out of the pot. I take it to that point and then back it off just a little. The length of the boil will depend on what's being boiled. Generally; a 60-minute boil is all that is needed for most brews.