Hi Tiffany,
Firstly, welcome to shuttertalk!
Before you go shopping for a new camera, it might be worth finding out exactly
why you are currently getting blurry pictures. Shooting technique has the most impact on how sharp or blurry a photo is, particularly at night-time or twilight.
It is very possible to spend $10k on a camera and lens and *still* get blurry pictures, and equally possible to take lovely sharp pictures with a very cheap camera if some care is taken.
You might want to check out
This Post where I compare two different camera phones to a DSLR. Although the DSLR is clearly a better camera, even a four-year old camera-phone takes sharp photos when used correctly.
Blurry photos are generally caused by one of four things:
1. Poor Focus. Is the camera focussing on the subject correctly? Is the
Depth of Field enough for everything you want to be in focus? If the subject is out of focus then it will appear blurry. Ironically, the "better" (more expensive) the camera and lens the more critical focus becomes due to a shallower depth of field (area of focus). This is a trap that often causes people to end up with many more blurry photos when they first move from a comapact camera to a Digital SLR because the compact cameras are a lot less focus-critical and the photographer now needs to be a lot more careful with focus. Also, every lens has a minimum focus distance. You might find your close-up shots are too close for your camera to focus. Different cameras do have different minimum focus distances, but if you end up with a Digital SLR then you'll probably need a specialist macro lens to shoot anything closer than a compact camera.
2. Motion Blur. Is your shutter speed fast enough to capture the scene sharply? Are there any fast-moving objects in the scene that might require a particularly fast shutter speed? The less light the camera has available to it the slower the shutter speed will need to be when shooting. If you are shooting something that is moving, the shutter speed may not be quick enough to "freeze the action" and you'll end up with motion blur. To prevent this you need to take steps to slow down the moving subject or speed up the shutter speed. To increase the shutter speed while still maintaining a good exposure, you need to either provide more light to the scene (open curtains, turn on lights, use a flash, etc), switch to a higher ISO on your camera, or choose a wider aperture on your camera. If you are using a camera that only has a number of "scene" modes, try choosing the "sports" mode - it uses a strategy to maintain the highest shutter speed possible for the camera.
3. Camera-Shake. Blur caused by camera-shake is similar to motion blur except it is caused by the camera moving instead of the subject. Like motion blur, the faster the shutter speed the less likely camera-shake is going to be an issue. All the motion blur fixes will improve this type of blur, but in addition you have a couple of extra tricks you can use. Firstly, if your lens or camera has a form of Image Stabilisation then you should make sure this is switched on. Image Stabilisation is thankfully quite common in many cameras these days and it really works! Secondly, you should do anything you can to stabilise the camera. If you have a tripod, use it. If you are near a table or wall, then rest the camera on it. If you are next to a wall, then lean against the wall to brace yourself. There are many little techniques you can use to assist with camera-shake, including breathing techniques or even just making a conscious effort to be still while shooting, but many of them require practice.
4. Digital Zoom. If your camera has Digital Zoom, don't use it. Ever. Really. It is nothing but deceitful marketing hype. Zoom is good only if it is Optical Zoom which is "real" zoom. Digital Zoom adds no detail and simply enlarges and blurs the detail that already exists. As long as you don't use it, it shouldn't cause any problems and isn't something that gets better with better cameras... just don't use it ever. If you need to zoom in further than your optical zoom allows, then simply walk closer to it. This is called Zooming with your feet.
Looking at these points above, buying a new, better camera may help you a bit with #3 by providing Image Stabilisation. It may also help a bit more with both #2 and #3 by providing better high-ISO performance or a wider-aperture lens, but it may actually cause you more problems with #1.
On the other hand, learning a good shooting technique will help you a lot with #3, and learning how to best use your current camera and "read" the scene could also help you a lot with all of these points.
Either way, buying a new camera is rarely a "magic bullet" when it comes to avoiding blurry photos. My neighbour is a classic example; he has bought 3 digital cameras because each one keeps giving him blurry photos. He now has a digital SLR which he says is even worse than the compact cameras he had before it. He never uses it. I checked each of the cameras and I can get perfectly good results with all them, but he just isn't willing to work on his technique.
Of course I'm making these suggestions without actually seeing any of your photos and knowing what you mean by "blurry photos". I might be way off?
If you'd like to post a couple of example photos then we might be able to help more. If you could include details such as the shutter speed, ISO, and aperture that would also really help.
Also, if you are interested in buying a new camera... tell us what kind of photography you are interested in. What kinds of photos do you like? Even links to existing photos from other photographers showing the kind of stuff you'd like to be able to shoot.
What is your current camera, and what do you like and dislike about it (apart from blurry photos)?
Do you want to shoot portraits? Landscapes? Sports? Macros? Indoor/night-time photography? Is weatherproofing/shockproofing an issue? A long telephoto lens? A wide angle lens? Does it need to be small and discrete?