I have a 7 string Washburn guitar with fixed bridge and 2 humbucker pickups.  I have 2 amps: a cheap Peavy backstage, and a Crate Taxi.  The Crate sounds so much better that I hardly ever use the small amp - but at least I know that the noise problem I am having is not confined to just the one amp.

I usually like to play softer music with a "clean" sound and the ever present 60hz hum in the amp drives me nuts!  Running the Crate on battery power helps a little, but the main source of noise is the guitar itself.  If I put my finger on the plug or any metal surface on the guitar wired to the shield of the signal cable (such as the screws that hold the pickup switch to the body) the noise is greatly reduced.  I took the plastic cover off of the back of the guitar and was surprised to find that there is absolutely no metal shielding inside at all - not even aluminum or copper foil.  Secondly, I noticed that there was an unsoldered black wire coming from the same hole that the pickup cables pass through.  I presume it must go to the bridge, because when I jumpered it to ground - and I touch the strings of the guitar with my hand - the 60hz hum goes away!  Weird!

Should that black wire be hooked up?  Would it be worth it to try to retrofit copper shielding into the guitar cutout?  Would switching to humbucker pickups that have a metal shield over them help?  Do I need to go to having a pre-amp on the guitar?  Other suggestions?

Sounds like a grounding issue.  The bridge should be grounded to prevent the hum when you let go of the strings.

Yeah, that wire shouldn't be loose. Can't tell you what it goes to, but look the guitar over for a broken solder joint.

And it would be a good idea to get some foil tape to cover the inside of the control cavity & access cover with.

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I am puzzled as to why that wire is not connected.  It doesn't appear to have ever been soldered anywhere in the first place.  It does seem though that it should be grounded.  I found some wiring diagrams for my setup here:  http://www.guitarelectronics.com/c=hPwxER9D5q3lTpzfeE3HMMsE7/category/wiring_resources_guitar_wiring_diagrams.2_pickup_guitar_wiring_diagrams/

It shows the bridge being connected to ground.  I was looking at the cutout where I would need to put the shielding foil, and it is irregularly shaped.  Seems like it would be hard to cut the foil to the exact shape and size.  But I saw some conductive paint that might be easier to apply:   http://www.stewmac.com/shop/Electronics,_pickups/Supplies:_Shielding/Conductive_Shielding_Paint.html?actn=100101&xst=3&xsr=515

Has anybody used this stuff?

I've got the same problem.  I think all three of my electrics do it though.  I'll have to dig out the other two and try them again to be sure.

Try to hold the tip of the loose wire while plugged in.  If it is a ground wire, the hum should stop because you will be grounding it.  There isn't enough current to give you a shock if it is not a ground wire, but I wouldn't put my tongue on it.