A layer three switch is "much" faster than most routers, and usually has more ports for less money. Getting 24 Fast Ethernet ports into a router would be ugly, extremely expensive, and would require a killer processing engine. L3 switches also operate at "wire speed," and most routers do not. L3 switches ain't cheap, but compared to a router rigged to accomodate the same functionality, it's a definate cost savings (with better performance).
Since L3switches can operate at L2 as well, you can set up groups of ports that route to other groups of ports...virtually the same as having a switch hanging off a router...but the L3switch is faster in getting the data through. A common application is to use the L3 switch to aggregate L2 switches in-use at the access level....but you should verify that the L3 switch has the necessary MAC-per-port capacity.
For the hard-core network administrator, that has to deal with end-users adding extra networking components (hubs under their desk, for example), an L3 switch would allow the admin to set 30 bit subnet masks to each end-users subnet (one subnet per user, each subnet having only one valid address for the end-user connection)(Doug/L3Guy once recommended this for our call center's network...you know them engineer types...always messing with the LAN).
There are a number of reasons to use L3 switches, but most of the reasons stem from the segmentation functionality.
AND (sorry for singing an old song here....) a poorly implemented L3 switch does way more damage to performance and administrative overhead than it does good. Like any major infrastructure change, it MUST be well-planned before the hardware ever hits the network.
One of the major considerations is when a WAN is immediately adjacent to a highly segmented network (especially if it's using RIP as a routing portocol). If the LAN has tens/dozens/hundreds of routed segments, and you fail to properly manage the routing protocol updates, then you're sending a great deal of (usually useless) traffic over the WAN and wasting a lot of bandwidth.
Bottom line: an L3switch IS a router, a really fast router, most of the time you can use it the same as you would a "traditional" router (there are exceptions, of course). The main role of an L3switch is segmentation, and all the good/bad things that segmentation brings with it. Routers are usually still desirable/necessary despending on the network design and policies(usually WAN access).
FWIW
Scott