Short scale (30.5" from nut to bridge saddle) is "easier" to play if you have small hands/fingers. They're a good learner's bass, especially for teenage girls, young boys, or for guitarists wanting to get into bass. Short scale don't have the sustain or "piano like" tone that good long scale basses have, and it's quite difficult to find a short scale bass that has a decent thump from the E string. Cons are that you have less string brands/types to choose from, and short scale strings are often not sold in your local music shop. Examples of well known short scale basses are the Gibson EB series (EB-0, EB-3 - solid bodies, EB-2 - semi hollow body), Epiphone Rivoli (semi hollow body), Hofner "Beatle" bass and copies (eg. Epiphone Viola), Fender Mustang, Fender Musicmaster, Gibson Les Paul Triumph/Recording.
Medium scale is very uncommon indeed. I think the scale length is around 32". Rickenbackers fall somewhere between medium and long scale, at around 33" scale (from memory)
Long scale (34" - 5 stringers are often 35") is by far the most common scale. Virtually every major bass manufacturer's best known models are long scale - Musicman/Ernie Ball (all of them) Fender Precision, Fender Jazz, Gibson Thunderbird, Gibson's current Les Pauls, Epiphone Jack Cassady, Lakland. The list goes on. Long scale strings are easy to buy in many different types and gauges.
Then again, bigger is better, so you could always try and find something with a 39" scale, like my Scroll bass