When you save for web, the first thing you want to do is make sure the image is tagged with the sRGB color space. Despite making some fairly large strides in recent years, web browsers still do not have ubiquitous and proper support for color management. A lot of digital cameras will use the Adobe RGB color space (either by default, or maybe you selected it). Adobe RGB is a broader gamut, and can potentially preserve more precise color detail, but it is not yet fully compatible with the web (or, for that matter, the average quality computer screen.)
If you upload a photo to the web that is tagged with a color space other than sRGB, it will often be rendered incorrectly by some browsers. Adobe RGB and Pro Photo RGB spaces will usually render washed out and dull in color (Pro Photo RGB images might even look practically grayscale.) If this is what you are seeing, you simply need to tag your images with sRGB.
If your photos do show up with the correct color, but otherwise look incorrect, then you are probably saving them with too much compression. JPEG (the most ubiquitous photo format, and what I assume you are using) has a configurable compression (or quality) level. What level of compression you use really depends on what is in the photo. For photos with a lot of random detail and no gradients, you can get away with quite a lot of compression before artifacts show up. However, if your photos have smooth detail, or more importantly gradients, then you will want to compress as little as possible. Gradients, which may be as benign as a simple blue sky, compress TERRIBLY with JPEG. If you have photos with a lot of sky in them, it is best to use compression settings over 90 quality. If you wish to eliminate artifacts from such photos entirely, then you should just go with 100 quality, unless you plain and simply cannot afford your image files being that large.
You should experiment with different JPEG compression levels for each of your photos. There is absolutely NOT a "one size fits all" compression level when it comes to JPEG. Eventually, you will get a feel for what compression/quality settings work for what kinds of photos, and you won't have to experiment anymore.