#1
I have two guitars, a gibson LP, and a fender stratocaster. Both guitars now exhibit a mild to serious hum when plugged in to my amp. This is the style of hum which goes away when you touch the strings. Both guitars do this. Neither guitar does this when plugged in at the store. I am positive that the fender has a good ground, as I had it worked on over the weekend to put new pickups in, and the guitar worked fine and quietly in the store. I don't know about the gibson's ground. Both guitars hum when plugged into either of my amps, a mesa boogie 5:50 express and a fender blues junior. I have changed cables. The hum is worse when my computer is plugged in. There is always at least some hum when I am plugged in at home. This is driving me crazy.

The guy at the music store, who I believe to be pretty knowledgable, is recommending that I spring for a Furman power conditioner. Has anyone had to use a power conditioner to fight hum, and did it work? I've tried the Hum-X gadget and it did not help.
Fender American Deluxe Stratocaster
Epiphone Sheraton II, Seymour Duncan Jazz and '59.
ESP Horizon NT II
Epiphone Les Paul Custom
Mesa 5:50 Express
Egnator Rebel 30
Hughes and Kettner Tubemeister 18
#2
a power conditioner could help, but its a relatively costly and complicated option. I use one live, especially in older venues, mostly to ensure that I have consistent electricity. though it certainly helps with hum, it doesn't solve it completely.

a cheaper route may be to get a noise gate. a gate, set to just the minimum effective threshold level will completely mute out the hum without mucking with your tone the way a noise suppressor would. that being said, if you need to run a fairly high threshold, you'll definitely get some strange sounds (chopped off notes usually) as a result