In most cases, yes.
You should first try to optimize the graphics on your website. Many GIFs look just as good with fewer colors, and many JPEGs look just as good with a higher compression level.
You should also analyze the HTML of your site. Make sure you use relative paths, so that images are not downloaded more than one time. Remove any extra spacing and when linking to other pages, use relative paths and not absolute links.
While many hosts already have it, you could also see if your host has mod_gzip installed. This can save you a lot of bandwidth.
Best of all, optimizing your page like this makes the user experience better as your site will load faster for them!