Other than exercising, what are some other ways a 19-year-old could take care of their body?

Take care of your teeth. It may not seem all that important today, but later in life, you don't want to be wearing dentures.  I'll refrain from posting pictures of people whose teeth are rotten or have fallen out (it's pretty gross, believe me). Practice safe sex. You don't want to die before your time.

Yes. Refrain from smoking. Smoking is nothing but one big fat negative. There is nothing positive that smoking brings to the table that other healthier options cannot give you. Refrain from binge drinking or any heavy consumption of alcohol. Refrain from taking drugs for recreational purposes. Yes, I know people will defend drug taking, particularly marijuana, but for optimum health, I don't see how introducing recreational drugs that serve no medical purpose for you helps you. Refrain from overeating or eating copious amounts of bad food/junk food/processed food. Select foods that are as close to the natural state as possible when you shop, and prepare a lot of your food at home as much as you can. Load up on veggies and grains in your diet, watch the red meat consumption, eat more seafood. Your stomach/GI system and your heart will thank you. Don't misunderstand me though-having some junk food is okay once in a while, you have to enjoy yourself. Just don't make those foods the default when you eat. Keep your weight stable. Studies have shown that obesity/excessive weight is the number one cause behind many health problems. Yes, you are exercising, but that is only half of the equation-your diet is the other half. So if you are consuming a lot of high fat, high sugar stuff, clean it up. More fruit and veggies, less chicken wings, pizza delivery, and fried food. Make regular visits to the doctors for yearly checkups that are commiserate with your age so that you can find and deal with conditions like high blood pressure, cholesterol, etc. Make regular visits to your dentist for twice a year cleanings and checkups. Your teeth will last a long time, but you have to take care of them. Brush and floss daily and rinse as well. Use sunscreen every time you are going to be exposed to the sun (which basically means any time you leave the house). This will reduce the signs of aging, and protect you from skin cancer. Get a pair (or two) of high quality sunglasses, particularly if you live in an area with a lot of sun. They will protect your eyes better than the cheapos, and help reduce the risk of cataracts as you get older. Moisturize your skin. There are a lot of options for men nowadays for moisturzing without the "girly" aspect to it. Take care of your skin, when you hit 40 or 50 you will be thankful. Your diet will help with your skin health as well. Get plenty of rest. Learn how to relax. Reduce the stress and worry in your life.

Sleep! Sleep is something people tend to dismiss. But it's the most important thing you can do for your health (within reason). And particularly when you're 19 - your body is still developing. Sleep boosts your immune system, boosts brain power and helps your body regenerate. Unfortunately, at your age, most people are thinking they can push it. Sure there are times when you'll have to stay up late. But now's also the time to set healthy routines that sustain your body for the long run!

Eat whole foods, lots of whole grains, lots of whole veggies, a little meat... no unfermented (liquid) milk. Butter should be organic from grass fed cows if possible. Raw Unfiltered oils (olive, cocoanut) Learn to COOK, learn to take joy in cooking.

Eat well and get plenty of sleep.

Floss daily.   No kidding, floss.    Don't be cavalier about getting hurt.   For example, they can fix knees really well, and it won't ever be as good as the uninjured "original equipment".    And, take the advice in the other fabulous answers.

Stay drug-free. Always take the stairs, and never use the handrail. Make sure you're getting adequate dietary calcium. Don't spend too many hours a day sitting down. Take frequent breaks from screen time to exercise your eyes. Get an annual health check-up.

Drink plenty of water, and have a healthy diet. Eat lots of fruits and vegetables of different colors. Plenty of Sleep, avoid taking medicines as much as possible ( specially for cold, fever, they don't work). All medicines have side effects in short term and long term.

Exercise your mind. Besides the body, the mind plays an important role in your life. It holds your memories, tells your body what to do, and it answers the questions you think of. (And more). So read a book, solve some puzzles, and teach yourself something new. Yoga. It helps the mind, soul, and body. It may seem like a "girls" thing but it increases core strength and flexibility which is important as you grow older. It also helps clear your mind and it calms your inner being.