I spent all day yesterday doing landscaping and home improvement. You might be able to guess what impact that had on today's energy levels. By the time I was ready to head out on my run, I was exhausted and my muscles were sore.
At that point, it would have been tempting to just take the day off. But that would have been a mistake. Barring some kind of injury or act of over-training, it's almost always better to do some exercise than none at all. There are a few reasons why.
First of all, a lot of being fit means making fitness part of your daily routine. The more often you can get out there, even if you aren't killing it every time, the more that habit becomes second-nature to you. Once the act of working out is fully habituated, rather than having to motivate yourself to just get out there, you can focus on motivating yourself to go the extra mile. That's not going to happen on your "extra tired day," but if you can use that day to reinforce the habit, you'll be more motivated in the future.
Second, even easy days have health benefits. If you're running outside, then getting some sunlight on your face in and of itself will boost your mood and your health. If you pair your workout with some basic stretching, then the additional day added to your flexibility routine will have almost as much of a health benefit as the run itself. And of course adding a few miles to your weekly total is never a bad thing, ceteris paribus.
Third, you can use the occasion to work on things you don't usually have time for. For example, I wanted to explore a new running route today, which is not something I get to do when I'm running for speed or time. If there are any weaknesses in your form, you can work on them during an easy run without having to jeopardize the integrity of a speed workout or long run. Perhaps you want to break in a new pair of shoes or try something different with your wardrobe. Now's the time.
If you're a diabetic, even a short, easy run will help lower your blood sugar - in some cases, it might even do so better than a harder workout. If you're looking to lower your blood pressure, burn some calories, lose weight, etc., then having an easy day rather than an off day will help push you toward your primary markers.
Finally, and most importantly, it's a lot more fun to get out and have fun than it is to sit around not having fun.
So get on out there.