Another couple of big ones I remember:
Sobig, 2003. In particular I recall that media was talking about Sobig.F - https://en.wikipedia.org/wiki/Sobig
Mydoom, 2004. https://en.wikipedia.org/wiki/Mydoom
Sobig, 2003. In particular I recall that media was talking about Sobig.F - https://en.wikipedia.org/wiki/Sobig
Mydoom, 2004. https://en.wikipedia.org/wiki/Mydoom
Melissa - https://en.wikipedia.org/wiki/Melissa_(computer_virus)
ILOVEYOU - https://en.wikipedia.org/wiki/ILOVEYOU
Anna Kournikova - https://en.wikipedia.org/wiki/Anna_Kournikova_(computer_viru...
Slammer - https://en.wikipedia.org/wiki/SQL_Slammer
And of course, the fastest spreading virus of all time, Sammy (which only effected Myspace profiles but still meets the definition of a computer worm) https://en.wikipedia.org/wiki/Samy_(computer_worm)
I don't think the media covers malware/viruses like the used to around the turn of the century.