At 8 years old your tires have reached their life expectancy. Most reputable tire shops will not remount or even repair a puncture on a tire that old. I would follow your car's manufacturer's recommended interval for oil changes, with a minimum of at least once a year. Best is to make sure you get in a few long drives so that the oil can get hot enough to boil off water and other contaminants. Short trips are really hard on cars.
Manufacturer's recommendations are wise for oil changes in my opinion. Especially for those harsh short trips. It's hard to see if you're actually doing damage or not until it's suddenly very expensive.
Tires, I *somewhat* disagree with the above. 8 years is more than most people will get under harsh circumstances (lots of heat cycles, exposure to UV & heat), but if you've got a car that's largely garaged/protected from the elements my experience is that quality tires (you get what you pay for with tires, don't expect much from $99 for 4 tire offers) can easily go longer. I've got a set of 12 year old tires now on one car (almost at the wear bars, expect to replace them by the end of Summer) and just recently replaced 13 year old tires on another car (down to wear bars, light cracking on the outside by the tread line, internally looked pretty much new, no rot). OTOH, my Mom had a set of tires disintegrate at 3 years old with tons of tread left. :-)
Vehicle type can also alter your risk. I drive small, light, low sportscars. I've had flats while in motion before (including one explosive event where a whole tread block departed the tire while in a corner). Other than some wiggling as I recovered from the explosive failure, losing a tire is not terribly exciting. I'm able to pull over and throw on a spare (or worst case call a tow truck) pretty easily. If I drove an SUV / pickup / large hatchback (like Honda CRV) I'd be a bit more concerned. Those are a *much* higher rollover risk in the event of a tire failure, and rollover events largely do not end well for anyone involved...
Tire shops do have a lot of incentive to sell you new tires, and risk does increase with age as they don't know the conditions of your car. Locally, it's hard to get a shop to patch *any* tire anymore...