openssl base64 <somebinaryfile
On the plus side, you do get a prize for suggesting it [1]
Something involving bulk binary data moving over a pipe which isn't an indirect redirection would be:
gzip somefile | ssh user@host "gunzip >somefile"
Although, again, there's a perfectly good -c flag to SSH that would do the same thing.
Probably the most common example of tool-to-tool binary communication over pipes is:
find -print0 | xargs -0
