My EX500 (500cc inline-twin) has a steel frame and swingarm and an aluminium engine. It weighs about 430 lbs and isn't very stiff (frame flex). A modern, all-aluminium 600cc (inline-4) supersport weighs right around or just under 400 lbs and is much stiffer. Similarly, a Ducati 749S, with its tubular steel trellis frame, weighs in at 435lbs.

http://www.motorcycle-usa.com/photos/600totalweight.jpg

steel is probably best in most cases.

titanium has a strength to weight ratio advantage over steel, but is softer and not as stiff (all other things being equal). it's also more difficult to work with.

carbon fibre isn't all that crazy of an idea. some model years of the audi a4 used carbon drive shafts, and afaik the only reason they stopped was that people want their bling in places where others can see it, not underneith the car. a carbon/kevlar composite would be less likely to shatter.