Rootkits are primarily developed for persistent privileged access to a computer so that other malware can remain stealthed and perform its job. They are usually used in conjunction with other types of malware in order to augment its power and abilities (think of malware that "keeps coming back" after you remove it or malware that you are unable to detect). That’s not to say that’s always the case, there are many variants of rootkits that incorporate various things like network redirection, packet sniffing, key logging, etc. along with their persistent privileged access. Because there are so many variants of rootkits out there it’s difficult to say what their "normal" patterns are since they’re always changing.
Rootkits are the worst type of malware you can get. Especially when they incorporate uncommon additional functionality. True rootkits can not be removed or even detected by most antivirus and antimalware programs (in addition to programs like Norton, McAfee, and Avast this includes MalwareBytes, HijackThis, Spybot, and other tools that aren’t classified as full antivirus software). This is because rootkits will commonly modify parts of the operating system in order to intercept calls, manipulate data that’s returned to programs, and change the way core functionality works. Intercepting operating system calls and manipulating events and responses can be done by using something called API/function hooking.
There are special tools designed for this process. Even then these tools don’t detect "all" rootkits, they look for common methods used by rootkits and if there’s a new variant of a popular rootkit that has had the internals developed differently it's possible that it’s using entirely new methods due to new security tools being available to users. Sometimes you’ll need to bring the system offline in order to detect and remove rootkits. Rootkit detectors/removers use their own custom developed methods and functions to scan the file system, look for network connections, look for alternate data streams, enumerate the registry, and scan the memory. This is a difficult process since it involves using NONE of the API’s that are provided by Windows to accomplish these tasks. This is what sets these tools apart from other generic malware scanning tools.
GMER - This tool scans for many hidden objects and looks for hooks. Interpreting the results and choosing what to do can be complicated because many items it can return are perfectly normal and can be a part of Windows or other safe software
TDSSKiller - This tool targets the TDSS/TDL4/Alureon rootkit family which are extremely nasty and have many variants. It’s extremely easy to use with the exception that it may find hooks or hidden objects that are completely safe
Sophos Anti-Rootkit - A good tool for general rootkit detection. Interpret results with care (just like the other tools listed)
Malwarebytes Anti-Rootkit - A popular tool that seems to be getting some good press and reviews. Currently in beta which can be risky for tools like this
aswMBR - A tool from Avast targeting TDL4, Sinowal, Whistler, and others http://public.avast.com/~gmerek/aswMBR.htm
chkrootkit - Checks for signs of a rootkit on Linux systems
rkhunter - Another Linux tool that scans for rootkits, backdoors, and potential local exploits