I use a square frying pan on a stove with no problem.  The key is to make sure you get a pan with good heat-transfer qualities.  Mine is a handleless square with very low sides, almost a griddle but not quite.  It's pretty thick aluminum on the bottom, so heat transfers well but with no sides it doesn't weigh as much as a normal frypan of that quality would.  We don't use a lot of oil in frying so this works for us.  I got it on clearance at Holiday Sports before they got bought out by Gander Mtn.

A square pan also works great for pancakes, enabling 4 larger 'cakes per batch vs. only 3 smaller ones in a round pan.