InnoDB is my default goto, TokuDB when on-disk size is a consideration, Archive DB for the exceptional cases where I need even more, rarely accessed, data on disk, and MyISAM for its full text searching capabilities (usually de-normalized from a backing InnoDB table). Those are the big ones.
There's also the NDB and Galara Cluster, but you want a specific use-case to justify the added complexity and overhead.
I've seen Blackhole used in production, but that was an odd one involving a... unique... replication setup. The CSV engine is pretty awesome for huge data imports, but again, pretty unusual for actual use.
