Regular oil and filter changes are the 2.7 engine's best friend. The 2.7 is a great engine, but it runs hot, and it is hard on the oil. Conventional oil should be changed every 3,000 miles. Synthetic oil, there are some folks here running it longer than 3,000 miles, with test results to justify it.
What happens is that the oil begins to form sludge when it is not changed often enough. This can clog the oil passages in the motor, and some of them are very small and easily clogged.
How to tell if you 2.7 is ok, or heading for trouble: inspect the area under the valve covers. If you see clumps of tar-like material everywhere, your engine has been abused in the past. If you see the components clearly, with a maybe a thin film of varnish, your engine has been well maintained and may go several hundred-thousands of miles.
The other thing to check is the condition of the oil in the engine. Pull the dipstick and look at the oil on it: if it is black and you can not see through it at all, get an oil change as soon as you can, that oil is too old. Even with conventional oil, at 3,000 miles, it should not be black. It should be somewhat dark, but you should be able to easily see through it.
The 2.7 water pump sometimes fails, letting coolant into the oil pan. It is a good idea to check the oil weekly. If your oil was clear and ok one week, and the next week it is solid black, and you notice the coolant level is somewhat lower when the car is cold, you have a slight leak from the water pump into the oil pan. If the oil is ever milky and whitish-looking, then you have a major leak of coolant into the oil pan.
Change the oil as soon as possible, check it every day until you get the water pump fixed. Coolant destroys oil faster than anything else.
For what it's worth, I had two 2.7-equipped Intrepids. I used conventional oil and had it changed the oil every 3K miles, and I put 230,000 miles on both of those cars and never had any problems with them. I di not even know the 2.7 had a bad reputation because my results with them had been so good.
I just purchased a 2002 Intrepid in perfect shape with 65 Km on the clock, I got it for a great price, and the story should have a happy ending, however and after all the dust settled I found out that the 2.7 engine has a design problem that causes it the seize with no warning. How bad is this problem and what can be done to prevent this?