Would be to buy the DVDs for past seasons and watch those on your computer. I do know Apple's iTunes store does offer some TV shows, I'm just not sure if ER would be one of them, and if it would cover the entire back catalog of episodes. Couldn't hurt to look though.
Those are about the only two legal options open to you. There are a few illegal methods I won't get into... Partly because it's against forum rules, partly because it's illegal for me to tell you, and partly because if you can't figure it out yourself, you probably shouldn't be bothering.
How can I watch old episodes of ER on my computer? Do I have to buy something or what? Is there a site I can download something to do this?