Ken, Good question. But what do you mean by exercises - dry land or pool based? For dryland there are three things I do specifically for swimming:
1) stretch (alas not as much as I should), but stretching is really important in swimming. The arm movements for all strokes need a high degree of motion to perform them well. Also when "you" get tired swimming your muscles tighten-up, the triathletes I swim with all exhibit a marked stroke degredation from half way through our practices. They swim a whole lot slower than they could do, because none of them has particularly good range-of-motion, and certainly what basic flexabilty they have (by virtue of swimming) is compromised because their muscles are fatigued.
2) Core (stomach) exercises, to swim fast (or faster) you need to integrate your core into your stroke. There's a lot that can be said about how you do this, but what you need is a strong trunk. So a daily set of stomach exercises is I think a must. Currently my favorite is with a small "medicine" type ball and I do trunk rotation exercises with it.
3) Finally stretch cord work. Basically these can be a poor-man's dryland swimming bench (like the versa-trainer). I freely admit I do nowhere near enough of this type of thing. But basically you can use the chords to focus on the front/catch, the insweep and tricep extension for back, free and 'fly, I haven't tried simulating breaststroke because it's not a stroke I swim (if at all possible). But a set of stretch chords is I really good (and really cheap) investment - just try 20-30 tricep extensions (the end point of most peoples freestyle is way too weak). Just some thoughts for you:)
I swim with a Masters group, and have developed a heart problem where I have to take a medication that governs how fast my heart can beat, so sometimes I get really tired, especially when I focus on my legs. I'm working with a trainer for strength training and balance. He emphasizes stretching a lot. Is there anyway I can improve my stamina?
I just saw this post. Sorry if it has been a while since you placed it.
I know exactly what you are saying. I'm finding that a combination of strength training, stretching and proper breathing techniques make a big difference.
If you are swimming freestyle, it is also very important you are able to incorportate proper breathing techniqes with an efficient stroke.
I'm still learning, so not to make myself out to be an expert by any means. I just started my second season in a Masters swim program, so now it is time to hone my technique.
I'm finding that 90% of the battle is technique.
We have a lady on our swim team who has MS. She was the top swimmer last year, logging over 120 miles. She is no weight lifter or marithon runner. What she does is relax and go with the flow. Something I've found very hard to do. It is acheivable, so hope is on the horizon.
I wish you well and hope your ticker gets stronger every day.