They're usually pretty stable, but they are lacking in features compared to current routers.
My WRT54GL has been deteriorating, with uptimes peaking at about one week, and two broken ethernet ports. I recently upgraded to a Netgear WNDR3700, which lets me escape the overcrowded 2.4Ghz spectrum (none of my neighbors use the 5Ghz spectrum, whereas I can pick up about 15 different APs on the 2.4Ghz channels), and helps switch my wired network over to gigabit ethernet (which all but one of my computers now support). The new router also has about 4 times more RAM, Flash, and CPU power, so it can run a wider range of software. At some point I'll probably also start using it as a file/backup server with a USB hard drive.
I've bought multiple WRT54GLs because of the aftermarket firmware available for that model, but really it's quite old these days and there are comparably priced alternatives with much better specs. If you're getting a new router, you should definitely look into something more recent; the WRT54GL is just dated now. My home WRT54GL finally crapped out after ~five years earlier in 2011. I bought a Buffalo WZR-HP-G300NH and loaded up openwrt and I'm satisfied with it (though I wish I would have known to put trunk openwrt on first; stable is not maintained very well, developers hint strongly at just using trunk).
I have purchased no less than five (possibly six) of them over the last eight years. After the third device failure, it ceases to be an anecdote and starts to become a trend. I would guess that the median lifespan of a WRT54G is likely on the order of 18-24 months.
Perhaps I was lucky but I have not had these problems. I have a wrt54g v2 from many years ago still chugging along happily. However, as others have mentioned there are modern routers with a sub $100 price that give you much more bang for your buck. Wrt54's were great for their time but I would consider them a bit dated if you are looking to purchase a router today.
At the moment maybe nothing but many older routers simply don't have the horsepower to keep up with faster internet connections. (say beyond 40-50Mbit/sec)
