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Scale length--what is this?

Scale length is the vibrating length of the string. Its also how your frets are layed out. You can measure scale length from the nut to the 12th fret and multiply by 2. 35" scale can be a benifit in that it may give you a tighter feeling B-string. It can be a downside in that the other strings are also tighter. When choosing strings, you need to make sure you get ones that are long enough (see strings that say XL or something).

Different scale lengths produce slightly different overtones and timbres. I personally prefer multiscaled instruments for the eveness of tension and feel, as well as a more focused sound (all IMO).
 
The longest Im aware of is Knuckle Basses at 39". I know Carl Thompson has done a few 38" scales. My Dingwall is a 37" scale on the low B, down to 34" on the G.

And yes, the longer the scale, usually, the longer the neck, allthough there are things to do to maximize the space available. Longer scale also means the frets are further apart, and can be a greater reach in the low end. Some people with small hands cant get around that. Double bass is usually a 41-42" scale though, so if you can play DB, you can likely play any scale electric without too much hassle.