How to take pictures in low light without getting motion blur?

I'm using a Nikon D3100. I like taking pictures when I'm at parties and what not and I never use flash. I realize that I have to set the exposure value to like 1/4 or 1/16 even to take pictures in low light. But I notice that when the exposure is this low and people are moving I get motion blur. How do I take pictures in low light conditions?

One word, monopod. Why do I say that instead of tripod? Imagine being at a party and needing to constantly move a tripod around.

Increase the ISO setting to at least 3200.

It is far easier to reduce the noise later using Lightroom or Noise Ninja than dealing with the blur caused by slow shutter speeds.

Sample photo shot at night at 3200 ISO

I agree with the other two… Monopod, higher ISO… AND a faster lens (the lower the f/stop number, the "faster it is). When I'm shooting low light situations without a flash, the slowest lens I use is a f/2.8 (but I prefer the f/1.4 and f/1.8's).

Uh, 1/4 or 1/16 is not the exposure value but the shutterspeed.

Anyway, if the lens or camera has VR, use it. It will allow you to sue slightly slower speeds while handholding the camera.

The other things is as fhotoace said, raise your ISO as far as you can. Noise isn't nice but it's atleast to some extent possible to reduce the noise in post processing, blur can't be fixed.

If flash is possible (i.e allowed and you can afford a reasonable flash), then get a flash. It's undoubtably different than a photograph without flash but if used correctly you can light your subject and freeze their motion (i.e no motion blur) without completely overpowering all the ambient light. Ofcourse you'll then have to learn how to use the flash so…

If you really feel that flash won't work for you or in the situations that you photograph (for instance if you're trying to photograph sports or concerts flash is often impossible) other than raising ISO, and using the smallest available aperture there's not really much more you can do.