Redundant Internet Connections?

We were thinking of setting up two internet connections at our office so that if one went down, the other one would keep us connected. In the end, we scrapped the idea because the introduction of DSL to our router was causing our normal latency through cable to grow, which was definitely not worth it. On top of that, cable has been very reliable, and the DSL cost was not worth it.

Latency problem

I would love to know if its possible to have two internet connections active where only the fast one is used unless it is unavailable.

Internet Service Related links:

Verizon DSL Blog

Comcast Workplace Reviews