How to delete multiple files at once in Bash on Linux?

Bash supports all sorts of wildcards and expansions.

Your exact case would be handled by brace expansion, like so:

$ rm -rf abc.log.2012-03-{14,27,28}

The above would expand to a single command with all three arguments, and be equivalent to typing:

$ rm -rf abc.log.2012-03-14 abc.log.2012-03-27 abc.log.2012-03-28

It’s important to note that this expansion is done by the shell, before rm is even loaded.