I'm one of those people who LOVES feeling sore the day after working out. I love to feel muscles I haven't felt in a long time - it makes me feel like I really worked it.
If you've gone for a run yesterday, and today your thighs and butt are so sore that you have a hard time walking down stairs, then you probably want to skip out on running for the day. You want to give your muscles a chance to heal completely and properly, if you don't, you could end up injuring yourself.
That doesn't mean you have to skip out on exercising altogether. Take it down a notch and maybe go for a short walk or do some stretching - the light exercise will get your blood pumping and actually might help to relieve some of your discomfort. Or use this as a great opportunity to work some other muscle groups. Grab some weights and work your arms, or do some ab or booty strengthening exercises.
Fit's Tips: The main point here is to listen to your body, and do what you're comfortable with. Obviously if you are in a lot of pain, you want to rest your body. You can take an OTC anti-inflammatory such as Advil (ibuprofen) or Aleve (naproxen sodium/naprosyn). Or you can take arnica or rub Topricin on your sore muscles. If a muscle is extremely tender, you can also ice the area to reduce swelling and pain. On the other hand, if you are sore all over, taking a hot bath or getting a gentle massage might be the answer to your body's prayers.