Something I'd like to plant firmly into your mind - If you're able to save up enough money to buy the things you want outright, credit will be of little use to you.
Many people find once they've accumulated very good credit scores by use of good financial habits, that they rarely end up using credit, and get little out of having a 'great' credit score compared to an 'average' credit score.
Of course, a lot of that would depend on your financial situation, but it's something to keep in mind.
As stated by others, and documented widely online, you don't need to make payments on a loan or carry a card balance to build your credit history.
Check your credit on a popular site, such as Credit Karma (No affiliation).
There, you'll see a detailed breakdown of the different areas of your credit profile that matter; things like:
- Your utilization: Keep this under 30% of your credit limits on cards for good scores, and 0% is okay too
- Your average age of account history - longer is better
- Your number of open accounts, and total accounts
- Your payment history - the number of monthly payments you haven't missed - Not having a balance counts too.
- The types of accounts you've had - Banks / Lenders may want you to have some actual loan history in your profile before some other types of loans, like a home loan, but not a requirement by far, and depends on the lender what their criteria are.
- Records entered against you like judgements, collections, bankruptcies, etc.
The best thing I could recommend is get a credit line or credit card, and use it responsibly. Carrying a balance will waste money on interest, much like the car payment. Just having it and not over-using it (Or not using it at all) will 'build' your credit history.
Of course, some institutions may close your account after X number of years of inactivity.
With this in mind, I'd say it's safe to pay off the car loan.
Read your agreement and make sure there aren't early termination / early payment fees for this.
There have been notes in the comments section's of question/answer's here about concerns with getting apartment. My two cents here: Most apartments I've seen check your credit for negative marks.
Having no credit history, and thus never missing a payment or having a judgement made against you, will likely be enough to get you into most normal-quality apartments, assuming the rest of your application / profile is in order, like:
- Good references, if asked for them
- At least 2.5x rent payment in gross income
etc, things like that. If they really think you're a risk, they may ask for a larger deposit (Though I'm sure in some areas there may be restrictions on whether they can do this, or how much they can do it) and still let you rent there.