I work out in the gym (my home gym and the "real" gym) regularly, have for years. But, it is not specifically to improve my bicycling. It is for overall fitness, to prevent osteoporosis and because I thoroughly enjoy weight lifting, etc. and like to see how much I can improve my strength and body through the weight lifting and resistance exercises. Sort of a competition with myself. I love to lift "Heavy" and push myself really hard to near failure. I do low reps and heavy (for me) weights.
My home gym includes a bicycle trainer and training videos, etc. I use the "Body for Life" protocols, among others. One of the best "bicycling" exercises at the gym is the back extensions machine, which I do at the full 300 pounds max. It is GREAT for my lower back, and helps with my riding a lot. I do a lot of "Abs" exercises at home, but don't have the right equipment for really good lower back exercises, hence the gym!
On the home bicycle trainer, I have variable resistance, and do "standing up" pedaling to a high resistance.
My home gym:
