Parsing lines from a live streaming website in Python
You'll have to periodically re-download the website. Don't do it constantly because that will be too hard on the server.
This is because HTTP, by nature, is not a streaming protocol. Once you connect to the server, it expects you to throw an HTTP request at it, then it will throw an HTTP response back at you containing the page. If your initial request is keep-alive (default as of HTTP/1.1,) you can throw the same request again and get the page up to date.
What I'd recommend? Depending on your needs, get the page every n seconds, get the data you need. If the site provides an API, you can possibly capitalize on that. Also, if it's your own site, you might be able to implement comet-style Ajax over HTTP and get a true stream.
Also note if it's someone else's page, it's possible the site uses Ajax via Javascript to make it up to date; this means there's other requests causing the update and you may need to dissect the website to figure out what requests you need to make to get the data.
I'm trying to read in info that is constantly changing from a website.
For example, say I wanted to read in the artist name that is playing on an online radio site.
I can grab the current artist's name but when the song changes, the HTML updates itself and I've already opened the file via: 
f = urllib.urlopen("SITE")
So I can't see the updated artist name for the new song.
Can I keep closing and opening the URL in a while(1) loop to get the updated HTML code or is there a better way to do this? Thanks!