Of course it is! Some of my favourite photos that I took are from a crappy little point-and-shoot I had back in the day before I started getting serious.
Of course, a point and shoot does have its drawbacks; you do have a lot less control than you do with a DSLR, but it REALLY depends on the camera you get. The point-and-shoot I just bought my mum, for example, has full aperture, ISO and shutter speed control. Definitely not as good as a DSLR, but DEFINITELY better than a lot of point and shoots.
Really, it comes down to knowing your camera and knowing the rules of photography. If you hand a seasoned photographer a point and shoot, they'll still be able to get quality photos out of it, because when it comes down to it, it's the photographer, not the camera. Yeah, there are certain things you can't do with a point and shoot at all (for example, I primarily work in Digital Infrared Photography these days, and that's impossible on a point and shoot), but in general, ESPECIALLY with today's technology, you can get very quality photos.
What I'd suggest is pick up some photo books or look at websites. Learn about composition and then read the manual for your camera several times. Learn to love it, get close to it, sleep with it under your pillow, you get the idea. Learn deeply about aperture, ISO, and other functions that your camera might have. You'd be surprised what difference this can make in your photos.
What you might notice is less range in your photos; I mean that sometimes, the exposure or the colours won't be as strong. This is because the size of the sensor in a point and shoot (the thing that measures exposure) isn't very large, so you might notice that your whites might be TOO white (blown-out) or your shadows might be compressed and lose detail. This is something that is the major problem with point and shoots, but there are ways to get around it.
tl;dr you TOTALLY can, just learn about your camera!
no subject
Of course, a point and shoot does have its drawbacks; you do have a lot less control than you do with a DSLR, but it REALLY depends on the camera you get. The point-and-shoot I just bought my mum, for example, has full aperture, ISO and shutter speed control. Definitely not as good as a DSLR, but DEFINITELY better than a lot of point and shoots.
Really, it comes down to knowing your camera and knowing the rules of photography. If you hand a seasoned photographer a point and shoot, they'll still be able to get quality photos out of it, because when it comes down to it, it's the photographer, not the camera. Yeah, there are certain things you can't do with a point and shoot at all (for example, I primarily work in Digital Infrared Photography these days, and that's impossible on a point and shoot), but in general, ESPECIALLY with today's technology, you can get very quality photos.
What I'd suggest is pick up some photo books or look at websites. Learn about composition and then read the manual for your camera several times. Learn to love it, get close to it, sleep with it under your pillow, you get the idea. Learn deeply about aperture, ISO, and other functions that your camera might have. You'd be surprised what difference this can make in your photos.
What you might notice is less range in your photos; I mean that sometimes, the exposure or the colours won't be as strong. This is because the size of the sensor in a point and shoot (the thing that measures exposure) isn't very large, so you might notice that your whites might be TOO white (blown-out) or your shadows might be compressed and lose detail. This is something that is the major problem with point and shoots, but there are ways to get around it.
tl;dr you TOTALLY can, just learn about your camera!