Most are common sense. A few - alcohol, drones, firearms - catch people off guard.
Campfires & firewood
Build fires only in the rings, grills, or fireplaces at your site - never on bare ground (unless a beach site is approved). Campfires are often not allowed at primitive sites, so ask at headquarters. Don't gather firewood in the park, and don't bring firewood from far away (it can carry tree-killing pests) - buy it where you'll burn it. Never leave a fire unattended, and drown it before you leave.
Alcohol - a Texas surprise
You may not drink or even display alcohol in a public place in a Texas state park, and all outdoor areas count as public - so a visible beer at your campsite is against the rules. Parks generally don't sell alcohol either (with rare, specially authorized exceptions). This catches a lot of first-timers off guard.
Pets
Keep pets on a leash no longer than 6 feet at all times outdoors (or in your car or a crate). No pets inside park buildings, and don't leave them unattended at your site. Some parks have extra pet rules.
Quiet hours
Keep noise down, especially during quiet hours (generally 10 p.m. to 6 a.m.). People come to hear nature, not a sound system - bring headphones and finish loud activities before quiet time.
Drones
Drones are basically not allowed. The only exceptions are a designated area at Martin Dies, Jr. State Park, or filming with a park permit. Otherwise, leave the drone at home.
Collecting
Take only photos. State and federal law prohibit collecting plants, animals, rocks, and artifacts. Leave arrowheads and fossils where they are, and tell a ranger where you found them.
Wildlife
Never feed wildlife - it's against the rules and makes animals act badly (and sometimes dangerously). Keep your distance and store food safely.
Firearms
Under Texas law, a person 21 or older may carry a handgun in a holster, with or without a license (this is called constitutional carry). One catch: some parks sit on land leased from the federal government, and there a handgun needs written permission first. Check with the park before you go.
Hammocks, fireworks & generators
Hammocks are allowed within your site using trees at least 8 inches thick and straps at least 2 inches wide - no screws or anchors, and not on park structures. Fireworks and explosives are not allowed. Generator rules vary by park (often off during quiet hours) - check your site.
Swimming
Many parks have lakes, rivers, or beaches, but most have no lifeguards - you swim at your own risk. Watch children closely and check park alerts for water conditions.
Geocaching: check with the park office (and get a permit) before placing a cache. And follow Leave No Trace: pack out your trash, park only in designated spots, and leave your site better than you found it.