Swiftness of operation, size, flexibility, the list goes on and on...for me though it's the continuity one gets with a 36 exposure roll. I shoot 35mm and 120 (occasionally 220) with people exclusively because generally changing film holders in my 4x5 takes too long (anything longer than the 10 seconds it takes me to grab my alternate body or film back off the work table is too long).
Also the overall mechanical layout of 35mm cameras is something I enjoy. It's rare for me to find a medium format camera other than my Hasselblad or Rolleiflex that just "sits" in my hand. My Pentax 6x7 is alright, but not as comfortable as the others, and doesn't come close to holding a candle to my Nikons (F4s and F3s) or my Leica M2.
And needless to say, fast lenses, fast focusing, and fast shutters. Time between photographs is negligible, on a MF or LF camera there is a delay.