| Not a grounding problem, it's a shielding problem. Your surroundings, especially when you're close to your amp, are full of EMI noise. 60-cycle hum from electrical circuits is filtered out by your humbucking or hum-canceling pickups. The hiss however is static "white noise" that's too random to hit both coils at once (which is how the hum is canceled).
First of all, realize that you are going to have a little hiss in any electronically noisy environment. You don't like it, play in a Farraday cage.
Second, however, that noise can be drastically reduced with the proper shielding. There are many articles in this forum and around the Internet on shielding a guitar. The basics are to line the inside of the control cavity, the control plate, and the pickup routs with copper tape or foil. Run a ground wire from the bottom of each pickup well to the control cavity and tack-solder it in place. Then run a lead from the shield to the ground lead of the output jack (if the jack makes good enough contact with the foil, you won't need that, but make sure the hot lead doesn't touch the foil). Reassemble the guitar and you're shielded. EMI noise, instead of going through the signal leads and the preamp circuitry and making its hiss, will instead follow the shield harmlessly to ground. Some noise will still enter through the pickups; there's little you can do about that except buy shielded pickups which will change your tone. | 
