Removing malware can be extremely difficult. Malware, by design, will try to make itself almost impossible to remove. The only guaranteed way to remove malware is to reformat your computer and reinstall - which will delete all of your files. This is a reason why backing up your data is crucial. Hard drive reformatting is a stressful enterprise without a good backup, but a minor time annoyance otherwise. 
In addition to restoring your computer or device to a previous state - you should change your passwords. 

Additional Resources:
How do I protect myself against malware.

Adware
Adware is essentially abusive advertising. This includes pop-up ads and "bundled" software such as browser toolbars. Some adware is innocuous advertising, but other instances of adware can potentially damage your computer or steal your information. It is never a good idea to knowingly install or click on adware. When downloading software, be sure it is not also asking permission to download additional software on top of the desired product and when browsing be sure to use pop-up blockers or script blockers. 

Ransomware
Ransomware encrypts a computer's data so that it is inaccessible without a password. The ransomware distributor will then demand a certain amount of money, sent through an anonymous method like bitcoin, in order to decrypt the computer. There is sometimes a time limitation for payment. After this time limit, the computer's files will be deleted. The best way to recover from ransomware is to recover your data from a backup. 
 

Rootkit
Rootkits allow access to sensitive files that usually are not modified by computer users - at least not directly. Rootkits can include viruses, worms, and Trojan horses. These programs will modify the computer, steal personal information, execute malicious files, and potentially create bots. Rootkits, unlike adware and ransomware, will typically attempt to stay hidden from the user.
 

Spyware
Spyware will record activity on your computer and transmit the data elsewhere. This includes login information, browser history, and potentially other information. Spyware will try to remain hidden so that it won't be removed. It can also modify security  and network settings.
 

Trojan Horse
A Trojan Horse will trick a user into downloading malicious software. These programs will pretend to be something else that you are trying to download, but instead will give someone else access to your computer to steal information and install additional malware.
 

Virus
Viruses are malicious programs that will attempt to spread from machine to machine. They can attach themselves to files and programs shared between computers in order to infect as many machines as possible.
 

Worm
Worms are spread through networks, finding security vulnerabilities in programs and operating systems to infect machines. They can damage your computer, steal or delete information, and install bots.

University Owned Machines
ITS provides anti-virus protection for Windows and Mac machines owned by the University of Texas at Austin. Please contact your Technical Support Contact (TSC) for help setting up your computer.
 
AMP can be used on university-owned systems at no cost. AMP is available for Windows, Mac and Linux operating systems. The Information Security Office considers AMP one of the most effective malware protection tools on the market and has seen marked improvement from campus units that have deployed it.
 
For more information please see AMP - Advanced Malware Protection.

Personal Computers
For Windows computers, we recommend Immunet. On Mac OS X we recommend either Sophos or Avast.