1. Certain control flow structures rely on continuations:

For instance, Ruby's generator implementation requires them[1].
Generators provide the canonical - most natural and convenient -
solutions for problems as typical as iterating over two or more Arrays
in parallel, simple suspended execution, resumable functions, and
others.


2. Existing 3rd-party packages rely on continuations:

For instance, the very popular and useful ruby-breakpoint package is
designed around continuations.


3. Certain possible features and packages need continuations:

The most obvious example is continuations-based web frameworks like
Seaside. The Ruby community has always been living on the cutting edge
of web technologies. Lack of continuations might prevent Rubyists from
pursuing one of the most interesting recent developments in
web-programming technology.

-Alder

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[1] http://onestepback.org/articles/same_fringe/