This list, like most lists, is quite subjective; and it excludes a number of rather profound influencers on modern philosophical thought, but such is the nature of lists—they stir controversy.
I am partial to Eric Hoffer for reasons which I’ll offer one of these days.
Copyright secured by Digiprove © 2011 James Ament 
Interesting list. A little heavy on classic thinkers, which is understandable. Paul? Can’t say I would have thought of Paul even though he makes a decent argument for the inclusion.
If the weight is on influence, then with all due respect to Aquinas why not replace him with Augustine? And how not to include Kant? As Mr. Morrison says, including Paul is odd, given his endorsement of what was “folly to the Greeks.”
Yes, Paul didn’t come to my mind; and Kant did immediately.
That list does miss a lot of great philosophers; but it’s bound to happen in a list of 10.
I’ll give a list of 20:
1. Socrates
2. Plato
3. Aristotle
4. Kant
5. Hume
6. Spinoza
7. Descartes
8. Locke
9. Aquinas
10. Leibniz
11. Hobbes
12. Kierkegaard
13. Nietzsche
14. Wittgenstein
15. Frege
16. Hegel
17. Berkeley
18. Rousseau
19. Russell
20. Augustine
Louis,
And yet even in a list of 20 there are still some that one might argue are missing, e.g. Voltaire. It might be easier to come up with 3 or 5, but then that would probably reveal those that have guided one’s own philosophy rather than a list of the greatest.
Jim