Because jellyfish are such weak swimmers they should be thought of as
plankton. I think that the only way to keep one for any length of time
is in a specialized tank called a Kreisel, which is a circular tank
with a circumrotating current that prevents the animals from becoming
trapped against obstructions. Do Google searches on "Kreisel tank" and
"Kriesel tank" (note misspelling) for more information.
There are a couple of other problems to think about:
1. Lifespan - Most jellies of a size appropriate for a home aquarium
are quite short lived. Don't be surprised if they die after only a
month or so. [The Moon jellies already mentioned have a total lifespan
of about a year in cold (10C) water, probably a good deal less in
warmer water. Plus, you really won't know how old they are when you
2. Food - Jellies of the appropriate type mainly eat zooplankton.
Copepods would be best but, since they don't live long anyway, you
might be able to get by with enriched brine shrimp.
Comb jellies (Ctenophores) are another possibility. They seem to be a
bit longer lived than jellyfish but are probably harder to feed since
they are smaller than jellyfish and have a more 'delicate' apparatus
for catching their food. We've kept these guys in our flow through
Kreisel quite successfully but I really have no idea what it is that
they eat exactly. Brine shrimp would be far too big and I even wonder
whether a ctenophore could subdue an adult copepod.