Advantages of Virtual Private Servers

Operators maintain full administrative access (root access) to their section.
Accounts are isolated (to some extent) from other accounts on the same server.
Hardware and network infrastructures are maintained by the hosting provider.
They're less expensive than dedicated server plans.

Disadvantages of Virtual Private Servers

They're more expensive than shared hosting plans, so they're cost-effective only if the allotted space is used.
Operators are responsible for some of the server-side administration, such as application installation and maintenance. Those who don't have the necessary skills may have to hire someone to administer their VPSes.
Hardware assets such as CPU, RAM, and Disk I/O are still shared. (it depends on what type of virtualization)
If you don't secure your VPS properly, it may be open to hackers.
VPSes of certain types (such as OpenVZ) typically do not allow the modification of the kernel. This can prevent the use of some software that does require kernel modifications.