If they offer you unlimited space, but you put too many files on their server, they'll most likely terminate your account. Its like being asked not to come back after you've eaten ten plates at an all-you-can-eat buffet. If they can't make money off you they don't want you in their diner.
When it comes to unlimited bandwidth you have to remember that you aren't really getting unlimited bandwidth. Hosting providers have to set a limit to the number of concurrent connections each site is allowed to have. Lets say your hosting provider allows you 50 concurrent connections. This means that only 50 people can be downloading files from their server at once.
Don't misunderstand what I'm saying, you can have MILLIONS of people on your site at the same time, as long as they don't all visit at the exact same moment. Once your site is loaded, the user looking at your site is no longer a concurrent connection. However if you have anything streaming in your site: files to download or video/audio, then as long as data is being served that counts as a concurrent connection.
The hosting plan that I have is through GoDaddy, which offers "unlimited" bandwidth with it's $14.95 per month unlimited hosting plan. However the number of concurrent connections they allow is only 200. Their cheaper plan allows only 50! They do not advertise this in any of their promotional materials, but this is the back-door way of controlling how much bandwidth you get without actually setting a limit. You really can have as much bandwidth as you can possibly use with only 200 visitors connected to your site at once.
I have a video on the main page of my site that automatically plays when you visit the site, for this reason every single user I have is a concurrent connection. So I literally can have only 200 users on my site at once. If my site starts getting over 200 hits at once I'll have to turn off "auto play" on that video. But I still have a half dozen vids on my site, so I am limited to how many users can be watching videos at the same time. If 200 people were watching a vid at the same time, my consurrent connections would run out and every other person who tried to visit my site would get a connection error.
However unless you have a lot of streaming content, audio, video, or large files to download, 50-100 concurrent connections should be fine for the average user.
One more thing to consider with shared hosting is that, in most cases, you are also sharing an IP address with dozens/hundreds of other sites. If any of those sites is blacklisted for spamming/phishing etc etc their IP could be penalized... but THEIR IP is YOUR IP! For that reason, some users choose to pay extra for a unique IP address. GoDaddy charges an additional $2.99 per month for unique IPs.
Chad Spillars
http://www.disneysubmarines.com/index.html
"Look I finally made myself a signature!"