Most people who train in martial arts for any significant length of time end up with some injury or another. Usually, it's not the end of the world or your training, but choosing how to deal with the injury can have a significant effect on your training.
Like I said in my earlier post, sticking to your routine is very important. You don't want to disrupt it if you don't need to. Something like a mildly pulled muscle or broken pinky finger might not warrant a total hiatus from training. Wrapping up the area, taking things a bit easier, and notifying your training partners of what to be careful of will usually suffice (assuming your training partners aren't going to be jerks and exploit your weakness).
However, if the injury isn't healing well or is severe enough to hinder proper form in performing techniques, then you would do yourself a favor by taking some time off of the physical aspect of training. For smart/good students, this time can be used to study your art on an intellectual level. Even showing up to class isn't out of the question. Most people probably don't see the value of simply observing a class, but if you are practiced in martial arts and have a good sense of body movement, then you can gain much from observing your instructor and other students as they attempt to perform the required movements for a class.
Now, some people try to push through the pain and train when they really shouldn't. Yeah, you might avoid some of the short term strength and coordination loss, but there is often a long term cost that young students in particular fail to recognize. I have enough minor aches and pains in my body to constantly remind me of this fact. I can remember where I got each of those aches and pains, and I also regret not taking it easy to let them heal properly. Instead, I'm left with a constant reminder of how stupid pushing through the pain of injuries can be. Don't get me wrong. Pushing through pain when it is simply your muscles or cardiovascular limits being met is great for improving. Trying to do 200 kicks with a broken toe is stupidity.
Don't be stupid. Train for longevity. Train in such a way, that you won't be crippled or highly immobile when you're 70 years old.