One method, and I believe it's probably the most popular (for straight redundancy) uses Virtual Router Redundancy Protocol (VRRP) or the Cisco flavor, that they call Hot Standby Router Protocol (HSRP).
They are not interoperable. HSRP and VRRP won't work together as a teamed pair.
Both operate basically the same way, and can be used for two OR MORE paths. For the sake of discussion, I'll use a pair:
Each router has it's assigned IP address (as it normally would). In addition, each router pair (or more) with VRRP/HSRP enabled presents a "virtual" router (it looks like one router) address (both IP and MAC). Of the pair, one router is "Primary" the other is in "standby." The Primary or Active router is all handling the traffic pointed to the Virtual Router. If that router dies, or the path goes down, the standby router engages and handles all of the traffic.
As far as the clients/hosts on that segment can tell...nothing happened, because their "Default Gateway" address is the Virtual Router's. They may lose the session, but many/most applications/protocols can recover or re-start the session. The key ppoint is that the clients/hosts can continue external connectivity without re-configuration (or new DHCP assignment).
That's the basics. Now it get's interesting (I s'pose).
At this point, many people reach the understanding of "Well, nuts! I'm wasting a whole T1 just sitting there doin' nuthin'." It doesn't have to be that way ..... because of VLANs.
If you have the same router pair, and they both have the same two Dot1q VLANs, you can make Router A the Primary router for VLAN "A," and Router B the Primary Router for VLAN "B" .... and each router becomes the standby router for the other. Now you have (sort of) load balancing to the two T1s, with a redundant path. I say "sort of" load balancing, because it is a manual process .... the amount of traffic will depend on which VLAN you assign to a particular group of hosts.
There are some other methods of getting redundancy, some pretty elegant (policy routing) and some pretty basic (parallel paths, same administrative distance, Cisco load balances). IMHO, the median .... the middle ground between complexity and functionality, is HSRP/VRRP. Recovery is very fast (seconds, at most), it's reliable, you can specifically control the traffic, it's mature, it's supported .... life is good. AND, as I mentioned before, there is NO reconfiguration of the host/client - he always sees the same "Default Gateway."
We used to play with this in the Lab a lot. It's a Good Thing. The only thing I like better is Virtual PVCs in ATM with a ~20msec recovery .... and ATM outside the cloud is (unfortunately) virtually dead.
In the above examples, I called the devices "routers" (because it's easier than saying "Layer Three (L3) device"), we can also be talking about L3 switches (which are really routers). We could also be talking about one L3 switch that's been partitioned into two logical port groups (you lose some of the redundancy - the single switch becomes a single-point-of-failure).
Most, if not all, Cisco and Nortel routers can do HSRP and VRRP (respectively). There may be other "real" router manufacturers (i.e., NOT SOHO) that will do VRRP. I think 3COM used to be VRRP capable before they stopped making "real" routers ... and their L3 Switches probably still support it. I don't know "fer sher."
FWIW / .02
Scott