Get a backpack. Put these items in it. Carry it with you wherever you go. You'll thank me later.

1: A towel. One of the small hand towels in your bathroom is perfect.
2: A sharp pocketknife. This will likely be the most-used item in the kit.
3: A roll of your personal favorite toilet paper. Anyone who's ever used a public toilet knows why I include this.
4: A novel, magazine, or a couple comic books. The next time you're in a waiting room at a dentist or something, you'll have something you actually WANT to read.
5: A pack of cookies or crackers, and a can of your favorite soda. Sometimes, a snack is all that's needed to save your day.
6: A pen or two and a pad of paper. The ability to take a note down at a moment's notice is never a bad thing.
7: Twenty dollars. You WILL end up needing it at some point when you're out and about, and your wallet is empty.
8: A roll of duct tape. Cliche as it is, it's also useful as hell.
9: Hand sanitizer lotion. Some places are just plain gross enough that you'll want it.

Feel free to add whatever other items you'll want on a day-to-day basis; this is only a baseline kit. Also feel free to post those items in a comment here, I may add them to my own personal kit.