There had been startups founded by college students, and many continue to exist even now. Some of them have been giants while some trend-setters. The giants category, I'm sure most of us are familiar with. Still lets start with them.
Apple: Power of two Steves coming together is Apple- Jobs and Wozniak started right from the design of PCBs and went on to build Mac and the huge company Apple Computer.
FaceBook: The Harvard student, Mark Zuckerberg came up with most popular social networking site of the day!
Microsoft: Bill Gates too a Harvard student along with Paul Allen started with creating faster processors. His company Microsoft holds the biggest pie of PC softwares(also IE has maximum share in browser world, yes even today!)
Dell: Michael Dell started business of upgrading computers, office location- dormitory. Later worked with Texas state for upgradation and eventually emerged the Dell computers.
Netscape: Mark Andreessen, the man behind Netscape, one time dominating the browser market started working of building it while still a student at University of Illinois.
Google: Larry Page and Sergey Brin. Their fascination about search engines and data mining gives us the best search results today.
Tripod: Bo Peabody and Brett Hershey from Williams college founded Tripod.com (now a part of Lycos). It offers domain registration, web hosting and webiste building services.
Livedoor: Livedoor started in 1995 as Livin' on the Edge, a web consultancy run by Horie and a group of student friends. Made series of acquisitions & entered the search and contextual advertising space in America later.
Let us move on to the other category.
Steve Huffman and Alexis Ohanian started social bookmarking and news site Reddit while studying at University of Virginia.
Joe Davy founded EvoApp, where he is also the CEO. He is currently pursuing bachelors from University of North Carolina. EvoApp provides enterprise applications which keep customers, employees, sales and marketing folks all on the same page. It is a tool to collaborate various communication info via various means like email and social media.
Michael Markarian and Alex Kravets founded Zaang, which has given birth to child company I Am Hungry(which gives collective info of deals at restauants in your city...city needs to be in US!), while students at Babson College. Zaang lets folks of common interest interact with each other not just by text but also pics, videos and audio. You can follow multiple things of your interest.
Suhas Gopinath, world's youngest CEO founded Globals Inc at the age of 14 (now he holds diploma in global leadership from Harvard University). His company offers wide range of solutions from learning management systems to offshore product development and web plus mobile apps.
GoCrossCampus (GXC) was mulitplayer, rivaly-based online game which had made students go crazy for it. It was founded by four students from Yale University in 2007. Groups of players fight virtually over real-world territories in attempt for regional domination.
This list is incomplete I know....but big enough to inspire students and experienced professionals as well!