"Fast" is relative, of course. But Canon makes lenses with an image circle sized for a 2/3" sensor that achieve 930mm f/4.7 (that's real focal length, not 'crop factor adjusted' which would be 3655mm f/18). These are field lenses for broadcast HDTV - for example, the DIGISUPER 100 xs is a 9.3-930mm f/1.7-4.7 lens, with a built-in 2x TC for 1860mm f/9.4, and it's an image-stabilized lens. It's a 10x10" lens (that's why they're called 'box lenses') that's 2 feet long and weighs over 50 lbs, and it can be yours for a mere $175,000.
Speaking of big lenses and baseball games, I ran across a neat video of these lenses (a DIGISUPER 75 xs) in use by cameraman Tom Guilmette, who shoots Red Sox games at Fenway Park (which I can see from my office, incidentally).
If you watch through to the end of the video, there's a great shot of a plane flying in front of the full moon taken at 1400mm (700mm w/ 2x extender).
While we certainly think photo gear is 'expensive', cinema/broadcast TV gear puts it to shame - his tripod head alone costs more than a 600 II.