General Cleaning and Maintenance
I have some basic maintenance regimes I follow based on as-I-play, weekly, and monthly schedules--along with spot fixing any serious problems I come across as I play my arsenal. I feel like the more instruments you own, the less organized you can be on this and therefore the more problems you end up fixing as you go. Wood moves, screws come loose, and strings age--so you ultimately need to at least check the basics on a semi-frequent schedule. Here's my basic run down for electric guitars:
Once or twice a month
Check all of the pickguard screws, pickup rings, jack plates, potentiometer nuts, and tuning machine screws and lugs to make sure they are tight. Takes less than 30 seconds on my Les Paul--and that's the most complicated guitar I own hardware-wise.
If I'm in need of a string change (and I usually am) and the fretboard is nasty, then remove all the strings and hit the fretboard with some naptha (common lighter fluid) to clean the gunk off followed up with some Gerlitz Guitar Honey--which is basically mineral oil--to keep the fingerboard in top shape.
Check the potentiometer travel for all volume and tone pots making sure to listen for any scratching (obviously you'd need to plug the guitar in for this part). Also, make sure all the volume knobs are secured tightly and won't come off through normal use.
Quickly check pickup height with a small precise ruler (kept in my case) to make sure that the pickup screws have not vibrated loose from my constant abuse throughout the month.
Weekly
Check to see if I need to replace strings, and if I do change them out one string at a time. Some people swap them all at once all the time, but I have found that the setup on guitars equipped with Tune-O-Matic bridges are easily disturbed, so I don't like to do this unless I need to clean the fretboard.
Wipe down the entire body and neck of the guitar, paying special attention to nooks and crannies like underneath the strings and the headstock--no polish though. I have had bad experiences with polish in the past, so I simply use a little distilled water and some naptha for the hardware. I often use a cloth to clean underneath the strings if I don't take them off. You can thread it through underneath the strings and wipe the dust off by sticking your fingers in between the strings.
After I Play
Wipe down the front and back of the guitar with a soft cloth when I'm done. I also attempt to prolong the life of my strings by wiping those down as well with a separate cloth. My fingers are quite oily, so I can decimate a pack of strings in less than a week if I play frequently.
Humidity and Storage
Relative humidity is important for any wooden instrument because wood is hygroscopic, so I make sure I have a humidifier handy in the winter months to make sure that my playing room doesn't get too dry. Dryer atmospheres can potentially cause finish damage on nitro-cellulose and polyurethane finished guitars as the wood shrinks. Anywhere from 30% to 50% are good numbers for acoustic and electric guitars. Don't make the mistake of thinking that humidity only affects acoustics though; electric guitars are made of wood too.
Since I have a couple of nice instruments, I usually keep the serious guitars that I'm not playing in their hard case--but cheapies like my favorite Tex-Mex Telecaster are often found propped up against my amplifier for quick access :D.
Should I loosen the strings to provide neck relief?
There really isn't any answer to this question from a best practices standpoint. Different guitar techs and luthiers will tell you different answers. From a physics standpoint, leaving a set of strings on for a very, very long time has the potential of bowing the neck, but remember you have the added support of the truss rod to maintain the shape. The only time I recommend that you loosen the strings is when you ship your instrument.
