In most cases, viruses can do any amount of damage the creator intends them to do. They can send your data to a third party and then delete your data from your computer. They can also ruin your system and render it unusable without a re-installation of the operating system. Most have not done this much damage in the past, but could easily do this in the future. Usually the virus will install files on your system then will change your system so the virus is run every time you start your system. It will then attempt to replicate itself by sending itself to other potential victims.
The normal effect a virus will have on your system is that over time your system will run slower. Also when you are using the internet your connection may seem to run slower. Eventually you may have trouble running programs on your system, your system may freeze, and in the worst case you may not be able to get it to boot up when you turn your computer on.