A lot of the avenues in regards to regionless players (good investment) have been covered, but I'll attack the home computer angle.
There is a chance that you may be able to play the DVD out of the box, but you would have to use VLC Media Player to do so. Reports suggest that it ignores the region encoding on your machine and will allow you to play it; however, newer models of DVD drives may enforce this coding more strictly.
That said, it is possible to change the region of your DVD drive, but you may only do it up to five times before it is permanently fixed to that region. Look up instructions specific to your operating system before continuing1, and I would personally avoid any instructions dealing with loading or updating the firmware of your drive unless you feel confident that you know what you're doing.
As with the other advice, investing in a regionless drive may be the best option, since it allows you to buy with more confidence, and reduces the likelihood that you'll worry about these sorts of purchases.
Because sometimes, just sometimes, your local distributor doesn't have the anime you want in the region you need it in. (I'm looking at you, RightStuf, and your lack of complete RahXephon...)
1: I wish I could help here, but I only run Linux and have only ever run DVDs on Linux. I also have a regionless BD DVD-RW.