As a long time service provider network engineer I appreciate network clueful companies and recommend none and packet.net.

Vultr advertises and supports anycast, if you're looking for a multi-location vps provider. Others will do bgp but it's a sales process

Yes, I'm using two different providers and sync them up using master-master replication.

For DNS I use DNSMadeEasy's DNS Failover feature that automatically fails over to a different IP address when it's unable to ping the server.

I, too, would be interested in info on any cloud providers that support anycast.

I'm no networking expert but packet.net has a page on this: https://www.packet.net/bare-metal/network/anycast/

I see benefit on using anycast for your DNS, but is anycast actually a better option than DNS load balancing for my site? The idea behind using anycast is to use at least two different providers, so having packet.net only doesn't really cut it. Also I can do DNS load balancing with any provider by using something like Azure's Traffic Manager, so I struggle to see advantages.

It's very uncommon. In my experience the database becomes the issue.

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.