NS and BackorderZone are both right. There are various ways companies go about their limiting, but ultimately, if you use any amount of resources beyond "negligible", your contract will be terminated. There are often hundreds or even thousands of websites sharing a single server; if you use anything significant, they'll cut you off. Usually they put strict limits so that you'd have trouble using much in the first place.
Personally, I would never pay for shared hosting, "unlimited" or otherwise. Proper VPSes are too inexpensive these days to bother with that nonsense. Take Amazon Web Services, for example: a micro instance is free for the first year. After that, it's still less than what you're paying, as long as you pay a portion up front. I reserved a micro instance with them recently for 3 years; I paid $100 up front, and the rest monthly. When the $100 is divided over the course of the three years, the effective cost is just over $5/month. I threw in separate MySQL and memcached instances for similar prices, but you could just host those on the web server. Oh, and don't forget CloudFlare for DNS/CDN, which is free.