Seeing as I'm one of a few people who own a TeddyBabe here, I figured I may as well start a topic related to care & maintenance.
Please don't actually try to feed your TeddyBabe... that's a disturbing thought!
Cleaning
Some people apparently go months without cleaning their TBs, despite sleeping with them nightly. I have allergies and happen to be a bit of a clean freak, so my TB is cleaned on a relatively frequent basis. I use a solution consisting of 2 capfuls of Woolite/laundry soap for delicates, a capful of downy, and roughly 28-30 oz of water. Spray the solution on the doll and wipe the doll down with a damp cloth.
You don't need to spray them with the entire bottle, mind you. Just enough to get the plush "skin" damp. The idea is not to soak the stuffing/filler!
Other TB owners have used Teddy Bear Cleaner/Bath by Gund (Build-A-Bear Workshop also sells their own variety), Oxyclean, and a variety of natural stain removers. Personally, the home-made solution works best, and the cost per bottle is minimal.
Repairs
I recommend keeping clear acrylic or white thread, and an assortment of smaller needles handy. A "seam ripper" or stitch puller is also essential if you don't want to have to cut the fabric; your repairs will be much cleaner if you use one. A very sharp razor blade and a steady hand will also do in a pinch. Also, a tube of Krazy Glue (or a hot glue gun) can be handy if eyebrows, eyes, or lips come unattached or need to be replaced.
My TeddyBabe is a "classic" 3'11" - 4'0" model, not one of the newer 4'4" - 4'5" models. EW doesn't seem to use precisely the same parts inbetween production runs and the internals of a TB aren't well documented, so keep in mind that some of these instructions might be different for your TB.
Pubic Hair
I haven't the slightest idea what EW uses for pubic hair on the classic TBs, but they definitely glue it on very well. I initially thought I'd remove the pubic hair, but I realized that attempting to do so when the doll was new would lead to damage. The hair will eventually begin to come off, I recommend waiting until then to remove it.
Simply pull very gently on the patch of hair/fabric, using a very sharp razor blade when it meets resistance. I also recommend using a fabric steamer to loosen the adhesive in tough spots, as small tears do happen even if you're very careful with the blade and removing the hair.
My recommendation in the future is to order the dolls without pubic hair and add your own later if you want it!
Wrist/Arm damage
Classic TBs can often have issues with wrist or forearm breaks. Following instructions at another forum, I opened the TB's arm at the wrist using a lengthwise cut along one of the seams. It turns out that there was no wire ring but rather a joint wrapped in teflon tape or some sort of plastic. I ended up having to extend the cut about 6" in order to have enough room to examine the malfunction and attempt a fix.
If you need to cut in to a TB try to keep the seam as small as possible. After my own experience, I recommend cutting shorter width-wise openings rather than lengthwise ones, as there's less sewing involved.