Is there any 'web-based' sql test environment?
You can't really test a query without the right underlying dbms, schemas (or databases), tables, constraints, stored procedures, and permissions, which tend to be highly application specific. (That is, not readily reusable among multiple users.)
Instead, the database world has grown up into database management systems that you can freely download and install locally. Then you can build and populate your own tables, and test your queries however you like.
Most of these come with both a command line interface and some kind of graphical interface. It's not clear to me what a web-based interface would give you that doesn't already exist in one form or another.
I think that, to do what you want, would require commercial licenses for Oracle, DB2, SQL Server, and Sybase. That's a pretty high barrier to entry for a free web site.
There are free "disposable" database servers like db4free and even MonoQL.
As far as the web-based interfaces and short URLs go, I don't think you'll have much luck.
To manage your data you have to stick to what is provided (usually phpMyAdmin or similar) and there is no short-URL to query mapping. One other caveat of such system is that (without the appropriate user permissions) one user could easily destroy all your test data -- and remember that (relational) database versioning is much more expensive than plain text versioning, so that's pretty much out of the question.
For non-RDBMS, I can think of try.mongodb.org -- but it suffers from the same problems.
Almost forgot, the Stack Exchange Data Explorer, lets you practice T-SQL queries (with permalinks).
PS: As a personal side-note, I think it's a cool idea and I would love to see something like that implemented, perhaps even mashed-up with SchemaBank or similar - that would be just awesome.
Try SQL Fiddle.
You can try your SQL query and execute/test it.