Kindle Serial Numbers
To confirm which Kindle you have, look at the serial number on the back at the bottom (for Kindle 1, it's under the back cover). You should also be able to find it on the Kindle packaging.
Since firmware 2.5, it is also shown in the Settings page on your Kindle.
It is also shown in your account pages at Amazon: Your Account/Manage Your Kindle/Manage Your Devices
B001 = Kindle 1
B002 = Kindle 2 U.S. (Sprint)
B003 = Kindle 2 International (AT&T)
B004 = Kindle DX U.S.
B005 = Kindle DX International
B009 = Kindle DX Graphite
B008 = Kindle 3 WiFi
B006 = Kindle 3 3G + WiFi (U.S. and Canada) NOTE: Some European cities may receive this serial number as well.
B00A = Kindle 3 3G + WiFi (Europe)
B00E = Kindle 4 NoTouch Silver (2011)
B00F = Kindle Touch 3G + WiFi (Kindle 5) (U.S. and Canada) [Mostly]
B011 = Kindle Touch WiFi (Kindle 5)
B010 = Kindle Touch 3G + WiFi (Kindle 5) (Europe)
B012 = Kindle 5 (Unknown) [If you happen to get your hands on one of these, please enlighten us!]
B023, 9023 = Kindle 4 NoTouch Black (2012)
B024 = Kindle PaperWhite WiFi
B01B = Kindle PaperWhite 3G + WiFi (U.S.) [Mostly]
B020 = Kindle PaperWhite 3G + WiFi (Brazil) (added 2013-04-20, packagers make sure to add B020 to list of supported devices)
B01C = Kindle PaperWhite 3G + WiFi (Canada)
B01D = Kindle PaperWhite 3G + WiFi (Europe)
B01F = Kindle PaperWhite 3G + WiFi (Japan)
D01E = Kindle Fire (Kindle 6)
D026 = Kindle Fire 2
D025 = Kindle Fire HD 7" (Kindle 7)