Spyware

Spyware can be several things. It can send every keystroke you type in order to get access to credit-card numbers and passwords. It can search files on your computer looking for the same. It might tell someone else about every website you visit. And this is if you're lucky

To help getting rid of spyware applications, you can use an application such as Lavasoft's AdAware and Spyware Search and Destroy

AdWare

Sadly some people mistake AdWare for Spyware. Just to clear up the confusion: Adware is simply applications that have a financial model where ads are used to keep the project going. An example is Opera Software's free version of its web browser, that recently got Ad-free as well.

Rootkits

A rootkit is a set of software tools frequently used by a third-party (usually an intruder) after gaining access to a computer system. These tools are intended to conceal running processes, files or system data, which helps an intruder maintain access to a system for purposes unbeknownst to the user. Rootkits are known to exist for a variety of operating systems such as Linux, Solaris and versions of Microsoft Windows.

Recently the Sony Digital Rights Management Rootkit has gotten much attention. This used a windows "feature" that allowed you to hide files using a $SYS$filename. Microsoft has promised to provide a tool to remove this feature. The Sony Rootkit was exploited itself, and viruses started making use of it to propagate. Much to Sony's dismay they efficiently installed this on amongst others the computers of Homeland Security.

Too help detecting rootkits you can use applications such as Rootkit Revealer from Sysinternals