No matter where you host your site, shared hosting means sharing. If any one user consumes inordinate amounts of CPU time, we have to step in.
That's the whole point. It's why it's cheap. In general, if somebody's not causing a high machine load, we don't care what you do.
If you're using enough resources to get our attention, your site generally won't run on even the cheapest dedicated servers. You'd need to be spending a couple hundred bucks a month to get a beefy server. Our shared hosting servers are buff, plus your databases and mail are handled by totally separate clusters of machines.
Bandwidth is a whole different story. We've got bandwidth out the wazoo and encourage you to use as much as you'd like. However, like any other resource we have to directly pay for, if you use more than your plan is allotted, we'll charge you for it. The overage rates are listed here:
From direct experience and what we hear from customers, we're more forgiving than most larger web hosts. We really only get involved when you're stepping on others' toes. But when you're using (and only paying for) shared hosting, it means you have to, well, share.