In fact, they don't always annihilate right away. For example, an electron and a positron may form a bound state called positronium. Positronium doesn't live forever, but a certain form of it can live for a relatively long amount of time, more than 100 nanoseconds! That may not sound like much, but it does show that matter and anti matter don't have to immediately annihilate.
A relativistic positron can annihilate in flight with an atomic electron in matter. The integrated probability for a 50-MeV stopping positron is ~ 15%. See pages 384-6 in Heitler "The Quantum Theory of Radiation" Fourth Edition.