If I recall, they do, otherwise they won't have such short lifetimes.
The simplest case is a meson composed of a quark and its antiquark, which will obviously annihilate itself.
Quark and antiquark of different flavor can annihilate themselves as well, and all you need is weak interaction to violate the conservation of flavor.
You can look up the lifetime of neutral pion and charged pion to compare their relative lifetimes.