There are as many accents in American English as in the rest of the English speaking world combined. The base accent in most cases is Irish (County Cork I believe), which is why the "R" is so pronounced. Some accents have ethnic European influences derived from English as a second language, especially New York. The area with the least accent is around New England (I think that's where it's from) which is almost unchanged Queen's (King's) English in some respects.
In some southern States the accent is not derived from another language so much as a lack of education and a general low literacy in the past, so you have words like creature that become corrupted into critter and negro becoming corrupted into...well you know what that became. It's interesting that this low education connection is maintained given that whites (the 'educated') are not allowed to use that word but blacks (the 'un-educated') can say it as much as they want to.
Americans seem to have a very hard time trying to get their tongues around the antipodean accents. Indian English seems to come easy, South African a little more difficult, and Kiwi a bit harder but for some strange reason Americans can't seem to tell the difference between a Kiwi and an Aussie accent and in both cases pronounce words in a very mechanical way (G'day mate is NOT pronounced Gidday (or, worse, Goo Day) mite but G Day Mayt). Many Australians were rather embarrassed when Americans said how perfect Merryl Streep's 'Australian' accent was in the film Evil Angels - to us she sounded like she was from rural New Zealand. Kiwi's pronounce six (6) as sex or chips as chups and have generally confused vowel sounds (which has led to the constant digs by Aussies that Kiwis share their sheep (in orgies) while we just shear them). Other times American attempts at the Kiwi/Aussie accents end up sounding like Cockney London types.