How frequent are side-chain reorganizations of various lengths? I'm wondering if anyone has collected statistics on how often reorganizations of side-chains with length 1 happen in comparison with lengths of 2, 3, or more.

Related: What is the longest chain reorganization that has ever happened?
Random reorganizations of length more than 1 are rare. To get a fork of length 1, you need two miners find a winning nonce at nearly the same time. To get a fork of length 2, you need the same (1) happen right after a fork of length 1 and (2) have those miners mine on different sides of the fork.

However, such fork happen once in a while. See this answer for some statistics. And even longer forks happen due to bugs in Bitcoin code, like this one in March 2013.