from my experience (fairly limited, not had "that" many wires fry, at least unintentionally):
7-10A seems like a good limit for 22 AWG wire (copper).
though, running 6A through 22 AWG, or 4A through 24 AWG, voltage drop may be an issue (AFAICT: for a pair, ~ 1v every 4 feet or so). in this case, you want thicker wire or lower current (if maintaining voltage is important).
for 24 AWG, 7A is about on the "starts getting hot fast" threshold, much over this and the wire gets very hot or burns up, so I stick more around 4A (where it stays pretty close to ambient), and has a little more room if things go over slightly.
for 22 AWG, likewise for 10A. would probably keep it more about 6A or so.
for 22 AWG aluminum (I have some of this), I have noted it seems to get hot slightly faster than 24 AWG copper. probably bad things would happen if used at 10A.
insulation may matter some as well, where I have some 24 AWG wire (from some CAT 5e) with some very hardcore insulation (it is unaffected by solder or flames), so it can get good and hot and the insulation doesn't notice (flames give maybe some soot, and it is unaffected if touched by a hot soldering iron).
however, some other wire I have has insulation which gets very gooey and sticky if it gets hot, and may blob right off the wire (leaving the conductor exposed) if it gets hot enough. this wire can't be pushed anywhere near as hard (need to try to keep it at near ambient temperatures). some of this may include the insulation melting if touched by a glue-gun, so care may be needed when hot glueing it, and the hot glue and insulation may end up merged to some extent (and contact with hot wires may leave molten plastic on ones' skin).
(well, and the inner-wire is often off-center and there are no markings on the insulation).