How can I brew link a specific version?

This is probably the best way as of 11.1.2022:

To install a specific version, e.g. postgresql 9.5 you simply run:

$ brew install postgresql@9.5

To list the available versions run a search with @:

$ brew search postgresql@
==> Formulae
postgresql                 postgresql@11              postgresql@13              postgresql@9.5             qt-postgresql
postgresql@10              postgresql@12              postgresql@9.4             postgresql@9.6             postgrest

==> Casks
navicat-for-postgresql

DEPRECATED in Homebrew 2.6.0 (December 2020):

The usage info:

Usage: brew switch <formula> <version>

Example:

brew switch mysql 5.5.29

You can find the versions installed on your system with info.

brew info mysql

And to see the available versions to install, you can provide a dud version number, as brew will helpfully respond with the available version numbers:

brew switch mysql 0

Update (15.10.2014):

The brew versions command has been removed from brew, but, if you do wish to use this command first run brew tap homebrew/boneyard.

The recommended way to install an old version is to install from the homebrew/versions repo as follows:

$ brew tap homebrew/versions
$ brew install mysql55

For detailed info on all the ways to install an older version of a formula read this answer.