So I'm seeing a lot of misinformation here, so I'll try and clear it up. This only applies to glass aquariums that are held together with silicone and that's it.
Today there are 3 aspects holding an aquarium together. The first is a thin bead of silicone that is sandwiched between the glass panels. This is what provides nearly all of the structual integrity and waterproof seal. This layer rarely has a problem. The second is another layer of thin silicone that is smeared along the inside edges and corners. This layer protects the first and reinforces the water-proof seal. The third is the rim. The bottom rim on most tanks simply elevates the bottom panel to prevent any sort of uneven stresses on the glass, while the top is generally used to keep the glass in place while it is siliconed together. It's also used to cover up the unfinished edges of the glass panels in an effort to save money. For the most part, the top rim provides little to no structual support, and many people have removed it to create a (ugly) rimless aquarium.
Now as far as resealing goes, if there is significant degradation, then I would look into resealing it. But it's pretty typical for that thin layer to separate and bubble up in a few places.