It is absolutely possible to have NO credit. Bad credit is a totally different story.
If you have no credit, you will need to obtain at least one reportable credit instrument and maintain it for a period of time. The key word here is "reportable". Simply getting an apartment and paying your rent on time will do nothing for your credit rating. The only items that affect your rating are those that are actually reported at least one of the three major credit bureaus (Experian, TransUnion, and Equifax). While your options for obtaining reportable credit are limited, there are a few ways you can do this:
1. Open a regular checking account, and a direct deposit savings account: Many banks will be willing to allow you to open a checking account even if you have limited (or non-existent) credit history. In addition, set up a savings account at the same time, and have a regular amount (a small amount is fine) transferred into in from your checking account. You may be required to keep a minimum balance in the account and may not immediately qualify for a debit card, but being able to list your checking and savings accounts (assuming you keep them in good standing) on a credit application is a mark in your favor. Also, your bank may be much more willing to extend a loan to you in the future if you've built a favorable history with them.
2. Apply for a Secured Credit Card: A secured credit card is an arrangement by which you pay the credit issuing company a specific sum of money (the minimum is usually around 300 dollars but can that can vary) which they hold as a form of collateral. In return, they will issue you a credit card with a credit limit generally equal to the amount of your deposit with them. You can then use the card to make normal purchases up to your credit limit. It is very important that you pay AT LEAST your minimum payment on time (preferably, your payment should be posted to your account day or two earlier than the due date) Using this card prudently for a period of six months to a year will raise your credit score by as much as 50-75 points.
3. Purchase a vehicle through the financing company of a major car manufacturer: Generally, while your local bank branch may decline your loan application based on lack of credit for an automobile purchase, you can still have credit extended to you by the financing department affiliated with major dealerships. (For example, if you are purchasing a car from a Chevrolet/Oldsmobile dealer, GMAC may be willing to loan you the funds for your purchase) Be warned that your interest rate will undoubtedly be higher than traditional standard car loan rates, but the extra percentage points are worth it if you build a favorable credit history as a result. Additionally, after a certain amount of time (2 years is recommended) your newly established credit history may allow you to refinance the loan at your local bank at a lower interest rate (and thus a lower monthly payment).
These are the three best ways to build/improve your credit rating. One other important factor that will affect whether a lender will extend credit to you without a good history is whether you have a consistent job history. You're much more likely to get a loan if you've been with one company for a period of time, and have lived in the same place for an extended period of time as well. It's also wise to stay away from offers that scream out "Repair your credit!" or "We loan to anyone". These deals are generally not worth the higher rates, fees, and hidden costs--and your favorable credit behavior may not even reported to the bureaus for consideration in your score.
The most important factor in building a credit history is TIME. Yes, it's going to take a while. At the VERY least, you'll need 6 months of favorable (even outstanding) credit behavior before you'll have new credit opportunities extended to you. Since you don't have any unfavorable credit items on your history, and are simply building new credit, you're already ahead of the game. Good luck, and remember to spend wisely. Your credit rating will follow you and impact you for the rest of your life.