There are a few ways to do it, some are quite expensive and the others may not work for you.
Multi-links from different ISPs: With the right router (Cisco 3660, with a lot of memory, or better) using BGP you can use 2 different ISP's and if either link is down the traffic flows through the other. You'll need other things and it's quite complicated to setup but that's why GOD made CCIE's.
Multi-links from the same ISP:
You can get 2 links from the *same* ISP and ask them to make sure that if one is down that the other will take over. In order to provide more redundancy you should ask them to make sure each link goes through different NOCs. Since both links come from the same ISP you shouldn't have different IP addresses. (can be bonded or multi-plexed)
Other:
There are also a few routers that will accept 2 broadband connections and do failover/load balancing but that wont help you with hosted domains and mail, it's more for people who share bandwidth and want 2 cable modems so they can download more (not faster because they're not bonded in any way) at once.
If I were picking the proper and best method, BGP is the way to go but it's also the most expensive and complicated.
Hope that helps,
FredUG