Hmm, I guess mine are:
1. The Fame Monster - Lady Gaga
2. Body Talk - Robyn
3. Catching a Tiger - Lissie
4. Kala - M.I.A.
5. Born This Way - Lady Gaga
6. Aphrodite - Kylie Minogue
7. Come On Over - Shania Twain
8. The Fame - Lady Gaga
9. 4 - Beyoncé
10. Robyn - Robyn
11. Up! - Shania Twain
12. Speak Now - Taylor Swift
13. Man on the Moon: The End of Day - Kid Cudi
14. Das Grosse Leben - Rosenstolz
15. Laundry Service - Shakira
And I think calling them my personal Greatest Albums of All Time isn't really right at all, they're actually like my favourite albums of my lifetime.