Yeah, now that you mention it, legs are pretty underrated in GH's design. Balance, stability and general Newtonian physics is
definitely not worked into the game very well. For one thing, look at the mass distrobution of some of the stock meks in the game. It's pretty crazy in some cases.
I most usually keep legs, though. You can stick stuff into legs, like backup sensors and ECM units (to mitigate the WTF-factor when your mech suddenly performs like crap when the main unit goes out). Not to mention piling up backup mounting points, or just sticking a bunch of overchargers and arc thrusters into them. And as Frumple mentioned, the rate at which you can turn with legs is a big advantage compared to skimming IMO. And running really isn't all that crummy once you fit overchargers. I'm not really much of a flyer; I prefer ground stealth/artillery combined stand-up fights on foot (the mecha's foot, that is) so this might just be a style-of-play thing. The Puma and Excel are some of my favorite mecha, for example. Another big thing to me is that it takes much more firepower to take out a leg than to damage just enough arc thrusters/hover jets to put that gerwalk solidly down on the ground, and that really scared me off gerwalks and flyers after a few incidents.
My late game strategy
usually involves a lot of armor and... what where they called? ... heavy missles? The kind the Harpy uses. Those things that are really expensive to restock, but worth their price. I sometimes store extra clips of them in my mech. That's for softening up armor. After that, let the DC20x10 Heavy Laser, Starburst Rifle (

) and Breaker Cannons finish the job. Or all the mariad of other miscellanious missles and lasers I stuck into the leg mounts and armors, if my main weapon goes out or overloaded ;-)
Nova Scythes.
Melee. Fu**ing. Everything.
That sounds like fun, too. I lol at how melee weapons can be stuck into weird places. One of my favorite early-game tactics is sticking a SF:1 mace into my mek's leg as a potent backup againts Strongarms and such.