Sometimes, you can add shells to an aquarium, but it depends on the aquarium and the shell. Aquarium water will usually dissolve shells -- ruining your shells and causing problems with your water chemistry. However, the changes to your water chemistry can actually make the water better for very specific fish. And there are alternatives that can work in any aquarium.
Shells and pH
Shells can radically change water chemistry. Salt is actually not much of a concern, since it washes off easily. However, the shells themselves contain calcium, which will leach out into the aquarium water. Calcium chemically buffers the water, raising the pH. This is not always a bad thing. Some freshwater fish come from water with a high pH, and thrive in such conditions. African cichlids, as well as many fish from Central America, prefer hard, alkaline water. However, this process will usually ruin your shells.
Ideal Tanks for Shells
Keep in mind that if the aquarium already has an alkaline pH, shells will dissolve more slowly, since the water may already be saturated with calcium. Brackish water aquariums and any aquarium with a high pH will dissolve shells more slowly. Additionally, African cichlid aquariums tend to feature decorations like rockwork, and shells do not look out of place in this decor. While it's ultimately a matter of personal taste, shells do tend to clash with some aquarium decor. For example, they will look out of place in a densely planted aquarium with driftwood.
Some African cichlids actually spawn in shells, so adding them to your aquarium gives you a chance to see this behavior in captivity. Several small African cichlids from the Rift Valley Lakes in eastern Africa live in the shells of freshwater snails, but will adopt marine shells easily. These cichlids are often sold as "snail shell cichlids." They stay smaller than most common African cichlids and are a little less aggressive, making them ideal for smaller aquariums.
If you like the look of shells, but don't want to run the risk of messing up your pH or ruining your shells, you can use fake ones. Pet shops sell a variety of plastic and ceramic shells. These shells have no effect on pH or water chemistry. Some resemble real seashells, while other look more fanatical with day-glow colors or cartoon character licensing. All you have to do with these shells is rinse away the pet-shop dust and place them in your tank. Cichlids and other shell-loving critters will usually adopt them readily.