My alma mater, Iowa State University, was founded in 1858... so that puts it waaaay out of the running for this list. In fact, all U.S. universities are nowhere near the top 10 (I know, go figure).

The 10 Oldest, Still-Functioning Universities in the World

1. Ahvaz Jundishapur University of Medical Sciences - Khozettan, Iran. It was founded around 200 B.C. by Shapur I, the Sassanian king.
2. The University of Al-Karaouine - Fes, Morocco. Founded in 859, the Guinness Book of World Records has recognized it as the world's oldest continuously operating, degree-granting university. (The Ahvaz Jundishapur University has not been continuously-operating)
3. Al-azhar University - Cairo, Egypt. It opened its doors in 975.
4. University of Bologna, Bologna, Italy. The first university in the western world was founded in 1088.
5. The University of Paris - Paris, France. An exact date is uncertain, but it was sometime around 1150. Teaching was suspended in 1229 and the university split into 13 different universities in 1970.

6. University of Oxford "“ Oxford, England. An exact date the actual university was founded is unknown, but it is known that teaching has existed since 1096. Oxford is the oldest university in the English-speaking world.
7. University of Modena and Reggio Emilia "“ Modena, Italy. It was founded in 1175 but has faded in and out "“ in 1338 the medieval university was replaced by three "public lectureships" but no degrees were awarded. The university was reestablished in the early 1680s.
8. University of Cambridge "“ Cambridge, England. It is, as you might suspect, the second-oldest university in the English-speaking world. It was founded in 1209.
9. University of Salamanca "“ Salamanca, Spain. Founded in 1218, this is actually the second-oldest university in Spain. The oldest, Palencia, is no longer in existence. When Christopher Columbus was trying to gain Royal support for finding a western route to the Indies, he presented his case to geographers at this very university.
10. University of Montpellier "“ Montpellier, France. It's been around since 1220 but closed in 1793 because of the French Revolution. It opened again under the Imperial University of France in 1808.

In case you're curious, the oldest college in the U.S. is much debated, depending on your definitions.

The College of William & Mary claims to be the first college to become a university.
Harvard says it is the "oldest institution of higher education in the United States".
Johns Hopkins says it's the "first research university in the United States".
The University of Pennsylvania claims that they are "America's First University" and Georgetown says that Jesuit teaching began in 1634, which would make it the oldest. The formal campus wasn't built until 1788, however.