1. 1000-3000 miles. Check your oil and filter. For basic oil, you'll need to to change oil every 3000 miles. With new synthetic oils, the urgency of an oil change is closer to 5000-6000, but an oil filter change is still necessary. Synthetic oils are only more resistant to heat and breakdown. Therefore, they can stay in your engine longer and will require the oil filter to do more of the cleaning work.
2. 4000-8000 miles. Check your air filter, fluid levels and basic car safety. Your air filter will get dirtier and dirtier by basic dirt from the air and particulates in the engine compartment. A dirty filter can cause poor performance and poor fuel economy. Basic filters are cheap and easy to replace. Moving to an aftermarket parts by companies like K&N and Green will improve performance and mileage with only a negligible cost increase. Check your fluid levels like coolant and brake/clutch fluid. If you can, check your transmission and differential fluids as well. Coolant is important to make sure you're not leaking and potentially causing extra heat buildup in your engine. A brake/clutch fluid leak can be dangerous for obvious reasons. A hard to engage/disengage clutch can be a sign of a leaky fluid line. Transmission and differential fluids are very important, but often go overlooked because of the difficulty getting to them. You could safely go 50000 miles without a change, but those who drive high performance cars or drive aggressively should change these fluids more often as it could become harder to shift and eventually can cause premature wear on gears. Basic car safety means things like your tire tread, suspension parts, brake pads and other bids that passively contribute to a road-worthy vehicle. Windshield wipers are another bit to check, but wear will be obvious when it rains.
3. 15000-20000 miles. More safety systems like lighting should be checked often, but making sure the systems are working and there's not an electrical problem (not just a bulb out) should be something to check if certain bulbs continue to break prematurely. More importantly, this is about the time you should be looking into changing your fuel filter. Random sputters or long start times could be attributed to fuel pump/filter problems. This is a simple fix, though getting under the car and having gas splashed on you is usually a deterrent to most people.
4. 25000-30000 miles. This is another good interval to check brake pad wear again and in most cases, a great time to replace pre-preemptively. Some also recommend a fuel injection service to make sure the engine is working at its peak. A liquid fuel additive can work wonders as a fuel injector cleaner, making sure gas is sprayed evenly and effectively in the cylinder. Also checking your accessory belts is another good thing to check. Any cracking or noticable wear should be noted and the belts should be replaced.
5. 40000-50000 miles. Timing belts! Cars with a timing belt should have that belt changed. It's a $300-500 job that can save you the cost of rebuilding a head. The timing belt connects the crank shaft with the camshaft. Should the belt brake while the vales are pushed out and a piston makes a full revolution and you'll have a bent valve. Do not neglect this. If you don't know if your car has a timing belt, as your dealer or search the web. Brake flush. The brake lines will get water in them over time and if you drive the car hard, the brake fluid can overheat causing fluid breakdown. Bleed the brakes or have a professional do it. Be sure to add the best fluid you can afford. Most cars are required to run DOT3, but DOT5 has a higher temperature tollerance and will last longer and work more effectively. Transmission fluid flush. Change your transmission and differential fluid. Every day driving will cause enough debris to get caught in these that the 50000 mile mark is as long as you want it to go before a change of fluid. Around this time you might want to check your battery. However, if all is running well and your car starts well, leaving it in would be reasonable. Lastly, if your car is handling is not up to par, you might want to get your springs/shocks checked. Poor handling can lead to accidents or poor ride quality.
6. 75000 miles. Around this time your exhaust system may start to see excess wear, especially in Northern states that see a proper winter. Your yearly emissions check will do a good job checking the quality of your system. If you hear rattles and squeeks though, you'll often need replacement exhaust hangers or replacement parts. These can be costly.
Of course, in the mean time of any of these intervals you'll get the standard problems that crop up. Broken starters, busted alternators and flat tires happen from time to time. Some things are prudent to fix before braking (brakes and tires, for example). If you drive locally 95% of the time, you can get away not being preemptive on things like an A/C compressor or a new radiator. However, if you travel often, getting regular preventative maintenace is a must. Keeping your car healthy isn't always easy, but it's more than worth the peice of mind and enjoyment of driving down that country road or highway and knowing you'll make it to your destination without any hiccups.
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