what phones can work on what networks?

[shadow-tech]

can some knowledgeable individual please point me to a list of what phones can work on a specific network. i dont mean a model of a phone but what carriers phones are compatible. like:
Alltel phones will work on: verizon, sprint
verizon phone will work on: alltel, sprint
att phones will work on tmobile,sprint

this is just an example of the info im looking for. i just made it up to explain what im looking for.

USA carriers off the top of my head:
att
verizon
alltel
sprint
tmobile
cricket
bell