Generally, a person should read the manual that came with the lamp (at least once) just in case there's something unusual about it that requires you to clean it in a certian way.
But other than that, what I do is..
Our lamps run pretty clean. When it's time to change out a bulb, I remove the old bulb (following safety precautions of course!)
Then I get 4-5 layers of paper towels, unfold them (lay them flat) and soak them with alcohol. I take one wipe only on one side of the reflector; unfold the paper towel (to get a unused side) and wipe the other side. The idea is to not use the same towel layer twice, and risk grinding in dirt. I try to spin my hand like a little film cleaner, picking up dirt and not using the same area of the towel. After those two passes, I get another clean fold and give it an overall cleaning, folding the layers over after a few passes for a clean side. When the layers stay clean, I give it a sort of "polish" wipe.
Before I put the new bulb in, I tighten all those big DC connections, because the heating/cooling cycles always seem to loosen them up. Then, I put the bulb in and spin it with the nipple (the place where the sucked the air out) facing me. In our theaters, that our "code" to tell others that the bulb has not been rotated. When it is facing away, that means someone rotated it.
With the new lamps we have, we have actually stopped rotating bulbs. The glass envelope does not darken very much, and there too little light to be gained, and too much to lose if a heavy-handed person gets in there. Of course, at another theater, it might be well worth the time. We never wipe off the regular dust that gets on a bulb, nor do we wipe off the reflector with a bulb in place. In some dusty parts of the world, this might neeed to be done, but not here in the northeast USA.
Actually, Osram suggests rotating the bulb in 1/4 turn increments (rather then 1/2 turns.) But with less time for maintenance nowadays, we feel the time is spent better elsewhere. YMMV.
I would feel _very_ uncomfortable with a bulb with 10,000 hours on it. My understanding is that the quartz glass could be fractured, and may explode even when cold, when there are too many hours on it. Even if the bulb is running perfect, I will try to get rid of it after about 6000 hours. Not many make it that far (usually they start to flicker), but some do.
I'm sure others have good ideas.......
My only comment is on the paper towels -- even softened as explained in the procedures, there is a potential abrasion problem there. We recommend a soft cloth -- t-shirt or diaper material, something like that in lieu of a paper product.
We also try and limit the use of any cleaners except when necessary to remove a stain. Normally, a light dusting with the soft cloth should be sufficient to get dry material off of the reflector.
For a competent projectionist, I do think it's all right to DUST the xenon bulb. Any accumulation of stuff will absorb heat, increasing the work function of the quartz glass it's sitting on. Any stain, accidental figerprint and such on the quartz envelope MUST be removed using alcohol with a cotton swab or soft cloth, using all appropriate care and safety measures.
Great topic!
Booth conditions will certainly affect what you do and how often you need to do it.
We have never had much of a problem with envelope blackening - this is really to minimise anode pitting.
General question -- after rotation, have many of you encountered increased flicker? Are you able to alleviate it after some hours of running? Do you increase amperage to get past any initial flickering after rotation, or does the lamp settle down naturally?
I'm curious because my own experience has had mixed results.

Unscrew the flat lens from the holder (note: I'm referring to the flat lens element and not the entire "lens" that is mounted into the turret).
Fire the lamp and motor. Adjust the left/right, up/down and in/out controls until you get a "bullseye", meaning a nice black center with white "rings" around the black bullseye. This will be fairly obvious and very easy to obtain if your reflector and everything is lined up properly. If you cannot achieve this, call your tech.
Put the lens back in place and switch over to scope. Crank down the in/out focus control until you have a "hot spot" of light on the screen. It should be roughly centered. Fine tune this side to side and up and down with the other two controls until it is centered. Now turn back the focus control until you have an evenly lit screen, as best as possible. Avoid dark corners and an excessive bright spot in the middle of the picture. That's it.
Note: be careful when doing this. You do NOT want to run the lamp through the lens for very long without closing the manual lamphouse douser (not the electric one) to let it cool. Depending on the size of the bulb, you shouldn't do this for more than 15 seconds at worst to 60 seconds at best on a low wattage lamp.
Of course a *vertical* bulb never needs to be rotated 
Aaron
Although you can do a pretty good job of focus and alignment "by eye", the final check should always be actually MEASURING the light level and uniformity on the screen with a screen luminance meter, to be sure it meets standard SMPTE 196M. With really large lamps, it's always a good idea to run a loop made up of dark scenes from an old trailer a few hundred times, to be sure you aren't causing heat damage to the prints.
Pat Moore did a very nice tutorial presentation about lamphouse alignment at the ITEA seminar in Los Angeles this past January.
ALWAYS FOLLOW SAFETY PROCEDURES, INCLUDING PERSONAL PROTECTION IN CASE A LAMP EXPLODES! Likewise, electrical shock is always a risk unless you "lock-out" the mains power and properly discharge any capacitors.
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John P. Pytlak, Senior Technical Specialist
Worldwide Technical Services, Entertainment Imaging
Eastman Kodak Company
Research Labs, Building 69, Room 7419
Rochester, New York, 14650-1922 USA
Tel: 716-477-5325 Fax: 716-722-7243
E-Mail: john.pytlak@kodak.com
If you do that you'll probably fry the print.
I mention it because I've seen this happen more than once.... Maybe there could be a better name that's less misleading to the popper jockeys like, "Don't push this F%$#ING button!" 
I keep this piece of film in my wallet just to demonstrate to people what happens if you mess with that button.
Check around. Maybe you could borrow a meter from an equipment dealer or service engineer, or share a meter with other theatres in your circuit/city:
http://www.kodak.com/US/en/motion/newsletters/notes/june2000/pytlak.shtml
If you have a good photographic "spotmeter", you can calibrate it against a known 16 footlambert standard as measured by a "real" screen luminance meter.
Adjusting luminance and uniformity "by eye" can be tricky. In general, "brighter is better", as long as you don't get so bright that shutter flicker is an issue, or get so much energy that you cause heat damage to the film (as in Randy's blistered film above).
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John P. Pytlak, Senior Technical Specialist
Worldwide Technical Services, Entertainment Imaging
Eastman Kodak Company
Research Labs, Building 69, Room 7419
Rochester, New York, 14650-1922 USA
Tel: 716-477-5325 Fax: 716-722-7243
E-Mail: john.pytlak@kodak.com
When doing a CFS, we just usually go for the most output we can get 'cuz they're so inefficient. On Christie it's a different story...
Christies are so efficient you probably won't need to crank them all the way up.
When I get the lamp focused I always check it again. Sometimes I even back off just a "hair" to be sure. THEN I set the "Don't touch this @#$%&^* button" controls.
When focusing a Christie I'd rather have it be just a hair bit dim than burn the film.
What size Christie lamphouse are you speaking of? Are any of these perhaps 6 or 7k units? I'm just curios as I've only worked with Christie's lamphouses up to 4500 watts, but even on a test I did with the lamp cranked down to a hot spot, there was no film damage.
The advances in quartz used in xenon lamps means the incidence of blackening is far reduced.
After a career of being a "rotator" 4 years ago I stopped and lamp steadiness has improved throughout the lamp life.
David
On the burning film issue, one consideration is additional filters. Some 4kw systems offer insertion type filters as an optional item and not standard in larger wattage systems. That filter makes a big difference in heat on the film, especially if the focus is too "tight".
It's always a good idea to run a loop of an old trailer with dark scenes several hundred times after any lamp adjustment, just to be sure you won't cause "hot spot" damage to prints, as in Randy's example.
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John P. Pytlak, Senior Technical Specialist
Worldwide Technical Services, Entertainment Imaging
Eastman Kodak Company
Research Labs, Building 69, Room 7419
Rochester, New York, 14650-1922 USA
Tel: 716-477-5325 Fax: 716-722-7243
E-Mail: john.pytlak@kodak.com
Actually, the damage I showed you was because the autofocus mechanism broke and caused a malfuction which fried the film.
There have been incidents of somebody flicking the switch and walking away, though. Just about the same amount of damage.
Rory
Pat Moore also noted that paper towels may be too harsh, and scratch the coatings. Like you, he prefers soft cotton. I guess lens cleaning tissue would work well too.
Edmund Scientific sells a variety of optical cleaning cloths and solutions for lenses and mirrors:
http://www.edmundoptics.com
http://www.edmundoptics.com/IOD/Browse.cfm?catid=250&FromCatID=174
I only thought of paper towels because our company would never pay for cloth towels, and you can only ask for cloth rags from friends for so long.
The old-timer who showed me how to clean the Ashcrafts insisted on using diapers.
By the way, maxi-pads (un-used ones of course) work well for cleaning the reflectors, and there always seems to be an abundance of them in the theatre storeroom.
For every "Yes, rotate", you can find a "No, don't rotate". There are about as many xenon lamps that never have their current changed since installation as there are lamps started at 80% of their nominal value and then adjusted upwards to maximum current throughout their usable life.
Change and removal policy is one of those things as well. Let the lamp go until it's too dark, or remove it at warranty plus 20 or 30 or 50%?
To me, the bottom line is: Is there sufficient light on screen? I try to equip a theatre so light levels at the end of a bulbs "normal" life will still be at (or damn near) SMPTE guidelines. That's really not too hard to do -- good old "headroom".
As long as the lamp a) strikes reliably, b) the quartz envelope is generally clear, c) the arc is steady (non-wavering), and d) there are proper light levels on screen while running within the operating spec's of the bulb, I'm not concerned if the lamp has 2000 or 4000 hours on it. I get very cautious with quartz envelopes that are dark or very cloudy, as I feel they become more of a hazard.
One guy's opinion, right?
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John P. Pytlak, Senior Technical Specialist
Worldwide Technical Services, Entertainment Imaging
Eastman Kodak Company
Research Labs, Building 69, Room 7419
Rochester, New York, 14650-1922 USA
Tel: 716-477-5325 Fax: 716-722-7243
E-Mail: john.pytlak@kodak.com