Plugin for YOURLS, tested on 1.7.

Append Query String does what it says - just add a query string and it'll be appended as-is. For example,
http://sho.rt/shorturl?query=value
would become
http://reallylongurl/blahblahblah[...]query=value.

NOTE: This appends the query string as entered to the long URL, minus the question mark - if you want your query string appended as an actual query string in your destination URL you need to include it in your long URL.

The company I work for uses a third-party ticketing system whose URLs tend to get out of control. I wanted to pass users a shorter link to their ticket/change request/etc, so that:
http://ITticketing.system/incident/show?query=number=INC00001
could be specified as:
http://sho.rt/inc?00001
instead of having to type:
http://sho.rt/inc?query=number=INC00001

1. In /user/plugins, create a new folder named append-qs.
2. Drop these files in that directory.
3. Go to the Plugins administration page ( eg http://sho.rt/admin/plugins.php ) and activate the Append Query String plugin.
4. Have fun!

Thanks to Ozh for YOURLS, and llonchj for the Query String idea.