Cycling is a great form of cardio as it gets your heart pumping but is easy on the joints. If you are a regular cyclist you should be aware of which body parts are working, which aren't, and which you need to strengthen and stretch to improve performance.
Regardless of whether you clip in or not, the bike stroke utilizes most of the muscles in your lower body, from your hips through your thighs down to your calves. But depending on your bike, seating position and riding style, you might be using some muscles more than others. Its important to stay on top of any potential imbalances and alleviate them by exercising underutilized muscles in the gym. Weight training can also help you ride longer as stronger muscles fatigue later. Try to focus on single-leg exercises to close any strength gap that might have developed from relying more on your dominant leg while biking.
Given the posture of biking, regular riders tend to be bent over at the hip, even when standing. That's due to tight hip flexors and quads. Its important to stretch these muscles after every ride to avoid injuries associated with chronic tightness. Here is our comprehensive video on lower body stretches.
Most of all, you need to develop your core. Cycling benefits from a strong core, but on its own doesn't develop those muscles - especially spinning where the balance component is eliminated. A strong core gives you a foundation to push against when pedaling and helps stabilize your hips so you can generate more power. Almost all core exercises are beneficial, but you want to stay away from focusing on your rectus abdominis - the "six pack" muscles. These muscles are already shortened by the bent over riding position, and exercises like crunches just exacerbate the condition. Instead you should focus on your transverse abdominis, obliques and erector spinae.
Lastly, be mindful of what biking doesn't develop - upper body strength and overall bone density. Bikers are at higher risk of developing osteoporosis as they have lean bodies from a non-weight bearing activity. To avoid problems down the road you should compliment your cycling with a regular fully body weight training program.