Founded on February 8th 1575. Leiden University is the oldest university in The Netherlands and became internationally prominent in the 19th and 20th centuries. Nobel Prizewinners who worked at Leiden include: Heike Kamerlingh Onnes, Pieter Zeeman, Hendrik Lorentz and Willem Einthoven.
Other famous scientists who worked at Leiden are:
Albert Einstein, Paul Ehrenfest and Christiaan Snouck Hurgronje.
Leiden University is pretty famous abroad, but within the Netherlands it is usually seen as just another university. The general universities in The Netherlands (Utrecht, Groningen, Amsterdam, Leiden) are all funded in the same way: by the government. Enrollment is based on the same criteria.
For some subjects Leiden really is the best (or the only) option. For instance the Leiden language department has courses on languages like Sanskrit, Indo-European Languages, Tamil and more. These languages can't be studied anywhere else in The Netherlands. But Utrecht has a Celtic languages program that's doing quite well and is unique world wide.
I'm studying world religion myself, and I do feel that Leiden program is the best: very balanced and it offers quite decent specialty options.
Still, if one is interested in studying medicine, Dutch law, European law, math, physics or psychology (to name just a few important subjects) - Leiden may not be the best choice. These subjects are taught in many Dutch universities. The way the subjects are taught can differ a lot, and Leiden does not have a reputation for having the best teachers, though personally I've had some great teachers.
All in all, if you are considering studying in The Netherlands, you may want to look beyond Leiden. Whether Leiden is the best choice really depends more on the subject you want to study than on its historic reputation.