If you're using something like Cassandra (C*), it's pretty easy to have replicated data to multiple zones in multiple clouds. RethinkDB has a similar replication system... there are many others as well.

Not all data models fit into a Non-SQL database though, and may work better in a more relational.. caching and read-only partially up, can be another approach.

Designing your data around this may be impractical for some applications, and on the small scale, likely more costly than necessary. Most systems can tolerate 15-30 minutes of downtime every couple years because of an upstream provider.