What are the most interesting examples of analogous evolution in nature?

I was recently thinking about how much we could learn even from a cursory glance at alien lifeforms, based on the presence of analogous structures like bilateral symmetry, sensation, cognition, respiration, sleep, etc. And then I thought, well we have radically distinct clades of animal life. Why not look there first? What are some amazing structures or behaviours have that manifested "twice" (or more) in nature, in radically different biological contexts?