Ah, these kinds of questions are always fun, albeit difficult to answer. Said answer would probably be prone to change from day to day, but if I had to make a proverbial stab in the dark right now:
10: Sunburn (One of the songs that comes to mind when someone mentions Muse.)
9: Invincible (As I understand it this song gets a lot of hate. Cheesy...maybe. I think it's nice though.)
8: Apocalypse Please (Great anthem.)
7: Hysteria (All your bass are belong to us.)
6: Butterflies and Hurricanes (If only more Muse songs had piano solos. I do so love when they give in to their Classical urges.)
5: City of Delusion (A style that suits them surprisingly well.)
4: Stockholm Syndrome (A wonderful riff and powerful song.)
3: Knights of Cydonia (Epic.)
2: Falling Away With You (Again, some might call it cheesy, but I find it poignant.)
1: Map of the Problematique (Everything about the song just clicks for me. It...affects me, somehow. And sounds so good.)
Even as I write this I am reconsidering. Argh. Stab in the dark indeed.
(I have not heard Hullabaloo or most of their b-sides, so I did not factor them in my deliberations.)