Recumbents are just a different way of approaching cycling. To give a quick list of pros/cons:
Pros:
+riding position. Can help riders with bad backs or wrists, and you certainly see much more in arguably greater comfort.
+usually less wind resistance and faster on the flats given the same rider.
+riding experience is just different and for me at least, much more fun and relaxed. Think street luge and the word "fun".
+novelty and uniqueness. In traffic I've found you are much more noticeable.
+not that I've experienced this, but I think you might be generally better off coming off a recumbent; there is less height to fall from and your feet are first.
Cons:
-less value for money. Recumbents are not mass produced in numbers like regular diamond frame bikes and are very poor value for money compared to diamond frame bikes in the same price bracket.
-storage and transportation. Usually recumbents will be longer than a diamond frame bike, and can be subject to restrictions on planes and trains, let alone if you wish to put one in the back of your car.
-no knees for suspension. When you go over a bump, if your recumbent doesn't have suspension, well, it doesn't have suspension. You can't "stand" up on a recumbent to lessen an impact. For this reason I don't like riding in high traffic areas where there might be quite a few potholes.
-no bunny hopping or jumping obstacles on a recumbent.
-unable to vary riding style. Recumbents need your legs to spin all the time -you can't stand on the pedals going uphill.
-rack compatibility. Though not true for all recumbents, oftentimes you will need extra rack adaptors to allow for rack mounting. You can of course figure that into your complete costs but nevertheless annoying.
-difficulty in securing the bike. Some recumbents present an issue when trying to lock them up.
-harder to repair punctures/maintenance. Some recumbents are harder to remove wheels to repair punctures, as well as being awkward to fasten in a bike stand.
Contentious cons:
-problems on group rides. If you're on a recumbent, it can be harder to converse with your friends if they are all on diamond frame bikes, let alone the sometimes illogical attitudes of dislike of recumbents by other riders (sorry, but true).
-heel overlap on some short wheel base recumbents (though this is an arguable point as some diamond frame bikes have toe overlap as well.)
-stability. Short wheel base recumbents may not be ridden hands off -but again, one might say that of some diamond frame bikes as well.
Though looking at the list of pros and cons it might be easy to write off the recumbent, I have to add that the benefits of riding position and what you see can be hugely offsetting to any cons. If I were to tour across the USA, I've promised myself it would be on a recumbent due to comfort and the fact I'd see so much more.
And of course you might need to grow a beard, a pot belly, carry a pure mathematics book with you and wear open toe sandals with socks to ride one too
I'm sure there are some other factors I've forgotten to mention as well.....