Learn English – Website giving pronunciations of English words recorded in different dialects

If you're into phonetics, Omniglot's Welsh language, alphabet and pronunciation guide seems like a good place to start. IDEA's Dialects and Accents of Wales has some thorough recordings. The text transcriptions are particularly useful as they mention features of that specific accent sample.

From a more pop-culture perspective (read: American), Catherine Zeta-Jones is Welsh and sometimes uses her Welsh accent in interviews and such. It is sometimes possible to detect the Welsh coming through when she speaks with an intentional American accent in movies.

From my experiences speaking with my UK friends about accent stereotypes, a Welsh accent could be considered the cultural equivalent of what a "country" accent is here in America. But we'd probably need a real, live Brit to corroborate or elaborate further.

As an aside, detecting the difference between an Irish and Scottish accent qualifies as pretty good? Come back when you're picking out Liverpool from Leeds. Okay I kid, but only slightly. :)

Have a look at this highly relevant paper:

Towards an automated classification of Englishes
by Søren Wichmann and Matthias Urba
from the Max Planck Institute for Evolutionary Anthropology (Leipzig)

Have e.g. a look at the tree-like structure on page 4, Fig. 3.1. (unfortunately the referenced paper therein doesn't seem to be available publicly).