Virtually all students at U of I own a computer, and many tote their laptops to classes, coffee shops, and libraries. While it may not be necessary to own a computer—there is no shortage of public computers on campus—students without computers will likely spend a lot of time commuting to and from labs, and will find themselves part of a small minority. The question is really whether or not to bring a printer: paying five to ten cents a page adds up when the bulk of your course readings are online, and it may be a worthwhile measure to avoid having to run to a lab to print out a paper at the last minute.
A good thing about going to a state school is the funding, especially when this funding leads to great computer labs. The residence hall labs may be a bit loud, but they are all adequately equipped; each one generally has a minimum of 20 computers, all with Internet access and a wide range of software. Although labs do get busy, it is rare for there to be no computers available. Several main buildings have computer labs, so wherever you are on campus, you will not be far from a computer and printer.