Oracle:Oracle introduced this in 10g. It is implemented in roughly the way I would expect and looks like it's pretty useful.
DB2:DB2 seems to have this capability in 9.7. NOTE that I have not checked to see if it was available in earlier releases. However, it appears you have to go through the XQuery interface. I'm not surprised by this, but a bit disappointed. I had hoped for an implementation more like Oracle's. I think that the DB2 way is going to be cumbersome for the average user.
db2 "with val as ( select t.text from texts t where xmlcast(xmlquery('fn:matches(\$TEXT,''^[A-Za-z 0-9]*$'')') as integer) = 0 ) select * from val"
MS SQL Server:
SQL Server, it seems, requires you to roll your own solution or look to some sort of 3rd party. I'm very surprised by this.
There are 3rd party libraries that appear to be pretty robust. One example can be found here: SQL Server Central article on RegEx in MSSQL Server
I suppose that they want us to use the full text search, which appears to have robust features, and address the same purpose. Still, just a bit surprised ...