This site has an archive of 1876 (as of today) samples of accents. People from around the world, with different accents — native and non-native speakers of English — reading the same reading passage. The passage itself is not particularly interesting or meaningful, but it’s fun to hear the differences. You can also submit a sample yourself (find out how here.)
Start off by browsing the language index. or the atlas, and choose one to listen to. It’ll look something like this:
On the left, you can see the information about the speaker: birthplace, native language, age, age at which the speaker began learning/speaking English, learning method, and number of years in an English-speaking environment.
And the site isn’t just for linguists or language learners; actors use it too!