You could store the images on the filesystem of your web server, then configure your webserver to serve them statically (if using Apache, for example, this would be done via the Alias Directive).
This would involve mapping URLs (e.g. mysite.com/img/) to a directory on the web server's filesystem (e.g. /home/images). Of course, your webserver will most likely be serving a directory by default, for example /var/www/, and you could simply store the images here.
Where you store the images (and how they are served) will depend on things specific to your application, such as security (note that if you serve a particular directory on your filesystem, any client could potentially download the contents).
EDIT As per your comment - This would depend mostly on the size of the available storage on your web server. Also keep in mind that you should use images of a reasonable size, and a compressed format such as PNG or GIF.