Believe it or not, I have seen a lease that required the resident to own a vacuum cleaner. I don't know if that is enforceable or not. But, the owners theory was that if the resident at least owned a vacuum cleaner, they might use it. Living close to the beach, a vacuum is the best thing possible to prolong the life of your carpet, keep it looking nice, and hopefully get more of your deposit back. Walking on the carpet brings sand from outside in. The sand falls through to the base of the carpet fibers, then as you walk on the carpet, it rubs against the carpet fibers wearing them done. Over time it breaks down the carpet fiber and causes the carpet to lay down and look matted. It always happens in the highest traffic areas first, hallway/entryway, as these areas get the most sand and the most traffic. By vacuuming just once a week, you can double the life and look of your carpet. I have seen apartments lived in by fanatical vacuumers and their carpet still looked brand new after 10 years. On the flip side, I have seen carpet ruined in a semester in student housing (more than just sand was spilt on the floor though).
Also, do you like to walk barefoot around your apartment? If you vacuum regularly the carpet feels better on your feet and the hard surfaces dont feel gritty. It also helps your apartment smell fresher.
So, my answer would be yes, you do need a vacuum cleaner in your apartment. You will enjoy your apartment more and possibly save a little money.