The Sadmind worm was a self-propagating piece of malware, It was first discovered on May 8, 2001 in china. Sadmind is designed to provide remote system administration operations and is installed by default with many versions of the Sun Microsystems operating system. It affected some big operating systems like Sun Microsystems Solaris(OS) and Microsoft's Internet Information Services (IIS) which is the world's second most popular web server in terms of overall websites behind the industry leader Apache HTTP Server.
Beast is a Windows-based backdoor trojan horse more commonly known in the underground cracker community as a RAT (Remote Administration Tool). It was created in Delphi and released first by its author Tataye in 2002. Beast was one of the first trojans to feature a 'reverse connection' to its victims and once established, it gave the attacker complete control over the infected computer.
Once connected to the victim computer, via Beast hacker can access victim's all computer file and directories along with the power to upload, download, delete or execute any file or folder.
ALIAS: Sapphire, Worm.SQL.Helkern, SQLSlammer
Slammer spread to over 90 percent of all vulnerable hosts in 10 minutes and infected around 359,000 computers total and according to London-based market intelligence the worm caused between $950 million and $1.2 billion in lost productivity in its first five days worldwide.4. Sasser (2004)
Sasser is an Internet worm that probably caused around $18.1 billions of dollars of damage in 2004. It was created by a Computer science student, Sven Jaschan in Germany first seen on last day of april. While there was no intentionally destructive payload, Sasser did cause many computers to slow down or crash, causing some high profile damage.
And was destructive enough to shut down the satellite communications for some French news agencies. It also resulted in the cancellation of several Delta airline flights and the shutdown of numerous companies’ systems worldwide.5. Bandook (2005)
ALIAS: Bandook Rat

6. Nyxem (2006)
ALIAS: Mywife, Hunchi, I-Worm.Nyxem, Blackmal, Blueworm, Blackworm
Nyxem worm was first found on March, 2006. The worm spreads in e-mails using an external SMTP engine. It sends itself with different subjects, body text and attachment names. The worm also copies itself multiple times to an infected hard drive. Blackworm is designed to corrupt data on infected computers on February 3, 2006, in respect to The Day the Music Died.
The most scary thing in this worm is, It can deletes your antivirus programs, if they are installed in the same directories as the ones specified in the worm's code. It can also delete the entries in the Windows Registry belonging to these antivirus programs, so these applications will not be run automatically the next time Windows is started.The worm also contains one GIF file which is used to make a recipient of infected e-mails think that the message was scanned by Norton Anti-Virus and no infection was found.

But its havoc ended soon and it gone off the records after October 26.
ALIAS: Small.dam, Trojan.Peacomm, Trojan.Peed, Trojan.Tibs, W32/ZhelatinBut soon after the Nyxem ended, a new virus has been discovered on January 17, 2007 named Storm Worm having the same functionality as Nyxem, It hides himself in a email attachments that had the following title line: "230 dead as storm batters Europe." Users that opened the attachment let the virus come in their machines. This virus infected around 10 million computers worldwide and after the computer is infected it could be used to launch millions of spam emails that would advertise Web links.
8. Conficker (2008)
The worm attacks the Microsoft vulnerability MS08-067 in Server Service which allows remote code execution. This vulnerability allows a remote attacker to run arbitrary code on the machine without authentication and take full control of the computer. Second, Conficker Worm uses the infected machine computing power to execute password brute force attacks to crack administrator passwords in the local network. This will allow the worm to spread through network shares as well.
7. Storm Worm (2007)

But it has also got some new features of stealing identity and according to the United States Federal Bureau of Investigation the Storm highly helped hackers in bank fraud, identity theft, and a number of other cybercrimes.
ALIAS: Downup, Downadup, Kido
Conficker is a computer worm targeting the Microsoft Windows operating system that was first detected 20th November 2008 affected more than seven million government, business and home computers in over 200 countries. 
The worm is said to have caused 9.1 billion in damage, mostly in Asia, South America and Europe.
New versions of Conficker came with the power to
-Blocks DNS lookups.
-Disables AutoUpdate.
-Kills anti-malware.
-Scans for and terminates processes with names of anti-malware, patch or diagnostic utilities at one-second intervals.
-Blocks DNS lookups.
-Disables AutoUpdate.
-Kills anti-malware.
-Scans for and terminates processes with names of anti-malware, patch or diagnostic utilities at one-second intervals.
9. Daprosy Worm (2009)
Daprosy was first observed in early May 2009 and first announced to public as Daprosy trojan worm by Symantec on July 2009 . This worm is a malicious computer program that spreads via LAN connections, spammed e-mails and USB mass storage devices. Infection comes from a single read1st.exe filewhere several dozens of clones are created at once bearing the names of compromised folders. The most obvious symptom of Daprosy infection is the presence of Classified.exe or Do not open - secrets!.exe files from infected folders.
The worm is known to destabilize, corrupt and even stall the operating system due to programming bugs. It appears that it is incomplete and was probably created by students or amateur Visual Basic programmers. As of October 2009 special scripts are available to remove it from infected computers but till then many Windows system were stalled.
10. Alureon (2010)

PCs become infected by downloading software also particularly off torrent sites and visiting certain posting sites
Other viruses that appeared during this period of time include:
2001: Anna Kournikova virus, Sircam, Code Red worm, Code Red II, Nimda, Klez
2002: Optix Pro, Slapper
2003: Graybird, ProRat, Blaster worm, Welchia, Sobig worm, Sober worm
2004: MyDoom, Netsky, Witty worm, Nuclear RAT, Vundo, Bifrost, Santy
2005: Samy, Zlob Trojan
2006: Stration, OSX/Leap-A, Stration (a.k.a. Warezov)
2007: Trojan.Tarodrop.E, Spybot.ATZN, Rustock.C
2008: Mocmex, Torpig, Bohmini.A, Koobface,
2009: W32.Dozor, Win32/Pacex.Gen, Win32/FlyStudio
2010: only one virus Alureon has been detected yet.