Unexplained ammonia spikes are our bane in fishkeeping. Last one I got turned out to be due to a large slug trying to munch on the algae in the tank and falling in.
There's a hell of a lot of ammonia in a slug.
Other common causes have been mentioned above;
sudden die offs of anything, from plant to fish
an established substrate (particularly a planted one) being disturbed and throwing up a lot of organic matter.
tap water, both for ammonia loads and other random toxins that hit the filter (the water boards have an annoying tendency to put chemicals down the pipes every so often to flush them, all human safe of course, but not tank safe).
chemicals from your house or hands, air freshener, plug in things and sun lotion are the popular ones (I lost a betta recently to a well meaning sole going crazy with their furniture polish in the living room, their own that they brought with them, we don't do aerosols).
lack of dechlorinator can also be an issue, but generally only a big problem with large changes or high levels (which is why some people get away with it.....for a while).
otherwise sudden shifts in parameters can mess with things, temperature, hardness, pH etc.
I know a lot of these don't necessarily apply here, but it's a good start list.
As for dealing with it, 1, remove the source, 2, fresh water, 3, more fresh water, 4, even more fresh water, 5, wait.
