On Campus; the Pros and Cons.
Pros: Living on campus allows for fellowship of school and classmates. It's where a lot of socializing occurs and it's a place where you meet life long friends. It allows for close proximity to school, which is a big plus! as you don't have to worry about commuting or getting a car. The residence halls are usually also very well secure; you usually do not have to worry about your safety.You sometimes do not have to worry about cleaning and cooking.
Cons: For the adult individual, living in the residence halls can prove to be a bit restrictive. Often times there are curfews. Spaces are small and privacy is very limited. In dental school, you will be studying most of the time and quiet is essential - residence halls get very noisy at times. Living on campus can also be an expensive option.
Off Campus; the Pros and ConsPros: Living off campus allows for freedom, versatility, privacy and space. Sometimes, living off campus can be less expensive than living on campus (just a little hunting will do the trick). Private apartments are usually quieter, and have fewer distractions and so provides an atmosphere more conducive to studying than on campus. You do not have to share amenities (bathroom, kitchen, etc). In the end, having a rental history is good for future apartment renting or buying.
Cons: If you do not do your research right, living off campus may be expensive. Usually you have to pay 1 month's security deposit and 1 month's rent upfront. You may need to pay utilities and furnish the apartment (the trick is to try to get all in one so that the rent covers everything). You have to find time for grocery shopping, cooking, cleaning and basic maintenance of the apartment. Living off campus means you have to commute to school. This often means that you have to get a car; with a car comes monthly insurance bills, gas, etc.
All in all, living on or off campus comes with it's advantages and disadvantages. Choosing one or the other is completely dependent on you; your personality, your personal preference and your budget.