Using grep on Mac-style text files

You can't change grep's behavior, but you can change the file it sees:

tr '\r' '\n' <file | grep foo

Also, \r line endings are legacy these days; OS X officially uses \n, although there are still things that haven't been updated. In particular, AppleScript still hasn't quite caught up, which also shows in its using pre-OS X file paths by default and requiring POSIX file to indicate OS X native paths; also, many Carbon applications still use \r, Carbon being a transition framework from Mac OS 9 to OS X.

A common legacy utility for handling line endings is flip. It does in-place transformation for files between Unix, DOS/Windows, legacy Mac line-end formats, and can also sample a file to let you know what type it currently thinks it is. It doesn't ship with OSX, but you can get binaries from the link as well as source.

In this case, you can first flip -u yourFile.txt to make sure it's using newlines and not linefeeds to demarcate lines, and then use grep on it.