One technical limitation on your artistic efforts is resolution, or how many dots per inch your graphic can be made up of. Standard monitor resolution is 72 dpi, which is what a web version of any graphic should be saved as. For comparison, quality printed output is 300 - 600 dpi. Graphics which have too much resolution will be displayed at a larger size on the net to compensate. Keep in mind that adding resolution is very difficult.
File size is another technical factor.
This can easily get large for graphics, particularly photographs. The file size of your graphics is a major factor in how long it takes your page to get from the web server to the computer which it is viewed on. If this takes too long people will not wait for your web page or graphic to load. Experimenting with a smaller number of colors can lead to an adequate tradeoff in graphic quality vs. file size. These are just a few of the challenges posed by the same technology which allows us all to communicate graphically.