The Ring (US)? It's much older than that.
I think when it really took off was "I Know What You Did Last Summer" and "Scream".
These films also include:
* An introduction at the start where they clearly show which stereotypes the characters are - the stoner, the jock, the slut (these ones always get killed), the nice guy (sometimes dies), the geek/goody two shoes girl (lives)
* At some point the girl will scream "just leave me alone", "what do you want from me?!" or "just f***ing die!"
* A party or social gathering where everyone is laughing and only the main character knows what terrors await them.
* Cheesy Nu-metal in the closing credits
For decent Horror films, have you seen "30 days of night?" I liked that, it was a bit less tacky than most. Also I like the suspense in "wrong turn".