I agree with other answers here that it is about shortness, not memorability.
A question that would have to be answered in design: Do you want these links to last forever? is.gd, for example, operates on the principle that a link lasts forever. This means that anyone using the service now can no longer get urls as short as when I started using it -- they've run out of short urls less than five characters long. This has the benefit that if you come across a link a few years from now, it points to the same url (which may or may not be the same page). Personally, I use services like this generally because I want to share a link, not save it, so I'd prefer to re-use URLs.
is.gd also creates a new short url for an address every time somebody asks for it -- it doesn't check to see if there is already a short url for this address. I would guess this boosts performance, but again, at the expense of using up short URLs faster than necessary.
Statistics -- you can see how many times the url has been used. You could conceivably track other statistics, too... user agent strings, IPs, etc. Worth it?
Custom short URLs? Allowing people to pick URLs helps them be more memorable, but the "good" URLs will be gone quickly. If you don't also give at least an option for a random/next-in-line URL generation, you're forcing your users to come up with something when many probably want a fast, short URL and to move on. If you do custom URLs, at least give an option for random. And don't expect many choice URLs to be left after a week of heavy use.