Other Fediverse protocols -- I believe either Friendica or ... I think Hubzilla? -- have some level of account portability.
There's a fairly long-standing request for Mastodon to support this. For now, you can have accounts on other instances forwarded to your primary.
While you can export and import your own follows, followers of your account won't automatically redirect to the new home.
Masodon content however will syndicate across the Fediverse, and even some of my posts from a now-dead instance can (occasionally) be found.
This information is outdated since October 11, 2019. You can move followers from one account to another in Mastodon 3.0.