Okay, some comments here I fear from people who haven't used them!
Undergravels can and do work extremely well, provided you know their limitations. They can offer extremely good levels of biological filtration. The silt that can collect in the traditional undergravel filter can actually work like an extra layer of biological media. The bacteria love the stuff! So provided you clean the thing periodically (once or twice a year) then it works fine. You shouldn't use a traditional undergravel filter for big, messy fish -- there'd be so much silt collecting too quickly to be cleaned away with an annual check-up. But for very small fish like neons, an undergravel can work well.
On the other hand, a reverse-flow undergravel is one of THE BEST filters possible for big, messy fish. Why? Because only clean water is pushed into the undergravel, and that water is pushed from underneath upwards, forcing silt into the water column where it can be sucked up easily by the canister filter. So you have the easy-to-clean external canister removing solid waste while the reverse-flow undergravel provides biological filtration. This is an excellent combination when designed and set-up properly.
The main limitations are these:
Firstly, undergravels are essentially incompatible with plants. Epiphytic and floating plants would be okay, but anything with roots is likely to do poorly. Even if such plants did thrive, chances are their roots would get in the way of water flow, reducing water flow through some parts of the gravel bed while increasing flow elsewhere. That's bad, and an undergravel with a "short circuited" flow of water isn't going to filter water adequately.
Secondly, undergravels dramatically limit your options in terms of aquascaping. Apart from a few rocks or roots, you need to keep most (80% or more) of the gravel bed clear and perfectly flat. Terracing, large caves, heaps of rocks, big bogwood roots and the like are all out of the equation.
So the ideal situations would be tanks such as small community tanks with plastic plants and a couple of ceramic ornaments, or else large tanks with big, open water fish such as South American cichlids or goldfish that don't care about decor much. The former example would be served well by a plain vanilla undergravel, and the latter with a reverse-flow system.
For situations where you want lots of decor, plants, live rock, etc., undergravels aren't good choices. These are the most popular ways to decorate tanks nowadays, and that's why you don't see undergravel filters very often. But in and of themselves, undergravel filters are not obsolete, and as I say, in some situations they could be good value, reliable filters to choose.
Cheers, Neale