But unless you're a track sprinter, weight training won't do much for your cycling speed. You can use it to address imbalances and add strength to improve your posture, which can make long distances more comfortable. And if you are older then weight training can help maintain bone density and muscle mass.
The only weight training I do in the gym is chest, shoulders, biceps, and core. It helps a LOT with long rides and I had better balance on the bike as well. I go to the gym 3 times a week and workout is only 30 minutes long.
to mindaugas: I would consider working out your back as well. Not necessarily for cycling purposes, but if you're working out your chest without adding muscle in the back, bad things can happen. I don't know exactly what it does, but my friend never worked oout his back while working out chest, and he had to get massive surgery for it.
lifting weights can cause inconsistencies, your body naturally favor one side of the other bla bla bla, when i was in college i swam and when i hit the gym, my back was the last thing i was worried about so i focused on chest and legs,arms. after an injury to my back it took me years to get strong again, being in your early 20's and wishing your were dead because of back pain isnt a fun one ( deteriorating disk with a small protrusion) it took me a long to be where i am now, point being creating an imbalance in your muscles is bad....