I regularly use a moka pot for making coffee, and I've heard different people tell me about cleaning it. The consensus does seem to be that I should never clean it with soap, just rinse it with warm/hot water, but some people insist that it should never be cleaned!
What should my moka pot cleaning routine be?
If you stop washing your mocha pot completely, you'll see a bit of a residue buildup on the inside of the pot from many past cuppas imparting their special oils to surface. This "seasoning" is said to protect the brew from any off flavors that might be imparted by the bare metal of the pot.
Whether this effect can be quantified by a perceptible difference in taste, I see no reason to part with tradition; it is a badge of honor and the sign of a well-used pot. At the very least, you are saving yourself a lot of trouble in having to clean it out each time. You can certainly clean the outside with an appropriate cleaner if the patina isn't to your liking, but I would just rinse the inside with hot water. Liquid detergents have a way of imparting their own taste, and dishwashers will can quickly oxidize aluminum pots like the Bialetti.
As Robert explained the residue that is accumulated by not cleaning to rigorously is generally considered to add to the flavour. However, this remains a personal choice as always. I personally always rinse the pot with hot water straight after I pour out the coffee. This gets rid of the 'worst' of the residue without preventing the oils to build up over time.
For long time storage you might want to clean the pot a bit more. Cooking some water through your moka pot without coffee is the way to go. You repeat this process several times until you are sure the water that comes out is just water. After this process it is a good idea to dry the pot as much as you can. This includes leaving the lower half on the stove with a little water until it has all evaporated. This prevents any mould growth as this is the most likely site for mould growth.
You can use a mild soap (Bialetti mentions this) to remove the oils, which over time will charcoalize and impart a bad taste.
Also, you should (say, weekly) remove the filter in the upper component of the moka and clean out the charcoalized grease; cf. this video for instructions on how to remove the gasket and upper filter.
Just rinse it with fresh water, doesn't need warm and doesn't need soap as you said. Very important, have it cool down on its own before washing it and pay attention not to rub the outlet valve with cloth - to avoid risking that the valve gets stuck, just use your hands gently removing coffee residues around the rubber rings and - very important - the screwing thread.
This is what I do... on the other hand, a good friend of mine has an old bialetti one cup size - the traditional one, not the fiammetta or similar, and some time ago made some coffee for me, I asked: "How on earth this coffee is so good, mine doesn't even approach this quality, it is almost an espresso" he said to me: "Look, I don't wash it, I let it cool down with the old coffee inside and I clean it without water just before brewing again... you must make coffee every day though"
I had a coffeemaker like it and it had been a gift from my aunt years ago and it worked wonderfully and had never been more than just rinsed with very hot water. Well, one day I decided that it needed to be thoroughly cleaned and so I began unscrewing this and scrubbing that and that's when I made a grave mistake. See, my pot was so old that the rubber rings were pretty much imbedded or stuck or had basically become old and brittle and probably needed to be changed (?), but I was young and dumb and I began scrubbing the main rubber ring (I remember there being only one) until it disintegrated pretty much and I had totally ruined it. So, this isn't as much of an answer to a question as it is a warning to not mess with things you know nothing about.
