DVD incorporates a technology called regional encoding, which is designed to prevent DVD's from different regions (Europe, North America, etc.) from being played back in another region (if the DVD producer so wishes). The reason for this technology is to allow Hollywood studios to release DVD's at different times (and charge different prices) in different regions.
DVD player manufacturers don't really like this technology, and they're probably forced to apply it to satisfy the demands of the Hollywood studios. This is why DVD players can be 'hacked' so that they can play DVD's from any region.
For the average consumer, they probably want region-free DVD's so that they can buy their DVD's more cheaply, or so that they don't have to wait for it to be released in their country. For cinema enthusiasts, they may want to get DVD's of other regions because another region's version of a film is better.
Very generally, region 1 DVD's (usually NTSC) are the best in terms of picture quality compared to region 2 (usually PAL), except for the earlier ones which were more highly compressed. An exception is the Back to the Future trilogy on region 2, which has utterly superb sound and picture quality. The Star Wars trilogy on region 1 is also meant to be superb quality (I haven't seen this though).
I've noticed only a slight but definite difference in picture quality when I've played my DVD's back in progressive scan mode (on a computer monitor through a software DVD player). People with better systems will probably notice an even greater improvement in picture quality. Note that this isn't a cable 1 v cable 2 difference or a CD player v CD player 2 kind of difference, but a real and precise one.
I've plugged this site a number of times but I'll do so again:
www.dvdscan.com (though it's doesn't seem to be working at the moment)