Granted the stove is so small i can put two burners under my kettle but... hey, I don't mind... and I also don't mind having to forfeit space to my brewery...
I have always brewed indoors, but I have a great gas stove that can boil 6+ gallons of wort. I don't think most people have enough BTUs in their burners to do it, though. I know some people have trouble bringing even 3 gallons of wort to a boil on their kitchen stove.
If your stove can handle it, it's a great way to brew!
I agree with Yooper, I would try to bring 6G to a boil and time it... see how long it takes to get to your important temps, for me I timed it from 60 to 150 to 170 to 180 to 212...
It's totally possible. I brew indoors quite a bit during the winter months up here in Canuckville.
If your stove can't handle the full volume (even after the tweaks in the link Revvy posted), you can always split the boil into two pots. Works fine, especially if you batch sparge.
I've done several 5 gallon AG batches on my electric range. I just use two smaller stock pots, as FlyGuy mentions.
I go as far as to collect half the first runnings into eacy pot, and then do the same with 2nd runnings. This way my gravity is about the same in each pot, so my hop utililzation will be normal and consistent (rather than reduced due to a high gravity like partial boils for extract).
plus the smaller pots are easier to cool down without a chiller (ice bath in teh sink) as well as easier to manhandle.