Kayaking is an interesting sport that can be enjoyed by persons of all physical capabilities. There have also been a number of handicapped paddlers in our sport, Team River Runner comes to mind. Many disabled paddlers have competed in slalom racing over the years as well. Paddlers come in all age groups as well from 4 years old to well in their 80's. Paddlers come in all shapes and sizes as well from the small and petite Risha Shamota to a previously large paddler that invented the sport of squirt boating and former club member - Jesse Whittemore. That said, you will really get more enjoyment out of paddling if you do some exercise on the side.
Let's face it, most of us need to earn a paycheck and only get to paddle on the weekends. Some of us are getting older as well. As we age, we lose some strength and flexibility. Flexibility is important in kayaking as it helps to avoid injury (and certainly doesn't hurt in rolling a boat as well). Unlike running, paddling is an upper body sport for the most part. The most important set of muscles are your abs and the core in general. Any good strength training book on abdominal exercises is a great start. The next order of business is the arms and shoulders. I highly recommend purchasing a small set of dumb bells, forget the bar bell. Go for light weight and high repetitions, you are aiming for endurance - not bulging biceps. Use really light weights for shoulder exercises. These muscles are quite small and easy to injure if you are not careful.
For cardiovascular exercise, jogging and strenuous hiking are hard to beat. Bouldering or rock climbing are great exercise as well. Try out the Billy Goat "A" Trail for a great exercise. I often hike in late Fall or Winter. The trails are not crowded, weather is cooler, and the views are spectacular. We have lots of great trails in the Baltimore/Washington area, check out Bryan MacKay's book for trip descriptions: Baltimore Hiking & Biking Trails. Biking can be a lot of fun as well and there are many local trails to choose from.
All boaters need to maintain decent swimming skills. I know the PFD will keep you afloat but you probably want to avoid a long swim if at all possible and that means aggressive swimming. If you have a pool membership, take advantage of that resource. For the rest of us, practice aggressive swimming across wave trains - perhaps at a lunch spot. It is a great way to cool off and really hone those rescue skills.
Flexibility - now there is a tough one. Most women maintain flexibility throughout their lives - this isn't the case for us guys. It really pays to warm up first before stretching those muscles. Wind sprints, easy weight lifting, tread mill are all good for getting the engine started. Start with gentle stretching, if it hurts - back off. Concentrate on your shoulders. Here is a great video: Shoulder Stretching. Here is a short article I wrote on warmup & stretching: Warm Up and Stretching To Reduce Injury.
Some exercises I find useful for stretching the torso while I am in my boat are paddling in a straight line while holding the boat on a 45° angle, do so on both sizes. We do this exercise in the Little Falls workout prior to our eddy practice in the Z Channel. I also like twisting my upper body to the side and sculling with both paddle blades. With today's smaller boats, you can also try to reach the end handles / grab loops on the front and back of your boat. Once you are more warmed up, try a practice roll or two which is another good stretching exercise.
Here is a great video on kayaking fitness: Kayaking Fitness.
Here is a great strength training regimen for your shoulders from Davey Hearn: Shoulder Routine.
This is a great article on strength training for paddling. In addition, the link on Rotator Cuff Training (and stretching) is excellent: Rotator Cuff Training.