Time warner does supply a modem but you have to pay a "rental fee". Only certain routers work with time warner. Actually, all should, but time warner has a "authorized modem" page here: i cant find the link. funny, i was just there. I copied the list however. Here it is.
Turbo, Extreme and Ultimate Service Plans
Vendor Model
Motorola SBG6580
Motorola SB6141
Motorola SB6121
Netgear CG3000D
Netgear CMD31T
Zoom 5352
Zoom 5350
Zoom 5341J
ZyXEL CDA-30360
Lite, Basic and Standard Service Plans
Vendor Model
Motorola SBG6580
Motorola SB6141
Motorola SB6121
Motorola SB5101
Motorola SB5101U
Motorola SBG901
Netgear CG3000D
Netgear CMD31T
Zoom 5352
Zoom 5350
Zoom 5341J
ZyXEL CDA-30360
The reason that they are split up is because of the speeds. It really shouldn't matter, but again, Time Warner wants more money, and they force you to buy certain routers for certain plans.