Assuming you have a series 2 tivo, you probably want to connect both the tivo and the slingbox to the network. For that you need a router so you can use private IP addresses (assigned by the router for the LAN) on each device on your network and a single leased public IP address for the WAN side of the router. The router should also be capable of keeping your DNS entry up to date on dyndns.org so you can always "find" your IP address should it change when the lease expires.

Either way, get the router. Some of the Cable modem, DSL modem folks are shipping combination modem/routers now anyway. I just switched back to DSL from Cable modem and Verizon/Hawaiian Tel sent me this overly complicated box that does DSL-modem/firewall/ethernet-switch/wireless all in one box. I had to figure out how to turn all that crap off and just connect it to my netgear wireless/switch/router. But if you don't have an existing router, this one may work for you. I don't recall seeing any dyndns update screens in there though.

Plus I agree with those that said you really do want the firewall there.

-David