The short answer is, yes they can, but there may be limits. Vegans don't eat any animal foods at all -- no meat, eggs or dairy. However, it's pretty much a myth that you need meat or animal protein to build size and strength. I'm not saying that vegans are well represented in elite, open competition in the strength and muscle sports, but for most practitioners, a well-constructed vegan diet can have nearly all the necessary constituents required for building strength and muscle, including sufficient complete protein.
The two dietary constituents naturally missing from a vegan diet that could restrict optimum performance are vitamin B12 and creatine. B12 is only available in animal foods but many manufactured vegan foods include B12 supplementation and so do multivitamins; so B12 is not really a problem.
Creatine, a natural constituent of the body and a proven bulking and power enhancing supplement in sports nutrition, is not found in plant foods and supplementary sources are derived from animal products. It's likely that the low creatine levels found in vegan and vegetarian diets could restrict performance in strength and power sports compared to non-vegetarian athletes, although actual performance comparison studies would tell us more.
Further information on vegan bodybuilding is available at Robert Cheeke's site.
Burke DG, Chilibeck PD, Parise G, Candow DG, Mahoney D, Tarnopolsky M. Effect of creatine and weight training on muscle creatine and performance in vegetarians. Med Sci Sports Exerc. 2003 Nov;35(11):1946-55.
When your body is recovering from power lifting there is nothing to substitute meat but for maintaining your physique there are plenty of vegetarian athletes out there. Tony Gonzalez who plays in the NFL eats 100% vegetarian which suprises most people.
Creatine is reportedly available chemically synthesised from non-animal sources, and thus suitable for vegans.