Seahorses are delicate but no more so than a lot of marine fish or inverts. I keep a mandarinfish in my 30 gallon, relatively new tank, something that most people dont recommend doing. However I have set up this whole tank around keeping the mandarin and have researched their needs intensely.
The same is true of seahorses. The hardest thing about keeping them is the feeding issue. Wild caught seahorses will only live on live copepods, which are tiny crustaceans that coem in on live rock and build up over time in your tank. In too small of a tank, not enough copepods will survive and the seahorses will starve. Or, there will be pods, but not enough of them, and the seahorses will run out. They cannot survive on brine shrimp alone as that does not give them enough nutrition.
Anyway, their needs are very similar to my mandarin. I would not put any other fish in with them, and would not have a tank smaller than 20 or 30 gallons. You want it full of live rock, as that is where the pods live and multiply. I also have tons of macroalgae in my tank in which the pods live. As a precaution, I have also set up a separate small pod breeding tank so my fish will never run out of live food.
If you are serious about getting seahorses, I would strongly advise buying captive bred ones. They usually cost a lot more than the wild ones but are much healthier and some of them even eat frozen food (in additon to the live food, of course). Also, wild seahorses are becoming endangered and I would really advise against supporting their collection.
Hope this helps a bit.

Also, in comment to the post above about the kids at the pet store being able to keep them alive, that doesnt mean anything. Pet stores get new shipments weekly, so you arent keeping them long term there at all. And I personally have seen many, many seahorses die in pet stores, from rough handling, poor capturing methods, and basically starving to death in sterile pet store tanks. Unfortunatley they have very high mortality rates. All the more reason to go with captive raised.