How can I find out if my DVD drive is region locked?

All drives slower than 5x never have any region code. 5x and faster drives may be region locked.
To test if your drive is region locked you need to download a small program called "Drive Info".

You can download Drive Info, here.

Now insert a region locked DVD disc into the drive, and run Drive Info. If Drive Info reports your drive as "THIS DRIVE HAS NO REGION PROTECTION" then you are in the clear. However, if your drive is listed as set to a specific region, then your drive is locked to that region. You may be able to change the region code up to 4 times, but after that your drive will become permanently locked to the last selected region.

When Drive Info reports your drive region code as "Not Permanent", it means that you have several region changes left in the drive before it does become permanent. It does not mean your drive is region free!