No, all participants in sports should not receive trophies. Sporting competitions are about results, not effort. Only those who have done the best should receive trophies, not simply everyone that has given their all. This may seem a bit cruel, but in life, results tend to matter over effort. Sports are no different.
A trophy gives some participants the extra drive they need to push them towards their winning goal. Parents should teach children at a young age how to be a good loser so they can be happy for people who accomplish their winning goals without pouting because they didn't receive their trophy.