Are you selecting altitude hold & what is you vertical speed set at. Are you using auto pilot to take off with if so dont. What I would suggest is to take off climb to about 1200 feet or so then engage the auto pilot. Make sure you select altitude hold and tha the veryical speed is below 1200 feet per min on 737 & about 1800  feet per min on 747's. Also set you auto throttle to 250 below 10000 feet. Once you have established a climb make sure your gear and flaps are up.

I never indicated that you did not know how to fly.
But a common problem is that some people try to use auto pilot to take off with & it is really not the correct use of the auto pilot. Another problem is people for get to engage altitude hold. I have noticed that some aircraft are very sensitve when autopilot is first engaged they try to climb at a very fast rate thus creating a stall. The default baron is a good example of this it trims like crazy until it finally settles in. I wound up changing the rate of climb down to 100 feet per min then ease it up once it stablizes. Before I did this the plane was all over the sky like a roller coaster.

One other note after you engage auto pilot keep an eye on your trim indicator to see if it trimming to quickly.
As I said when you engaged the autopilot in the default baron you could watch the trim knob start turning down rapidly. And it would keep it there casuing the stalls. There is probably another way around this but I just changed the rate of climb to 100 ft per min. Now when I engage the auto pilot it does not try to trim so much. I then set the rate of climb back slowly to around 750 to 800 ft per min. and have no problems.

Regarding your comment about the plane taking a dive well into the flight - I came across this problem once too, during a flight from Johannesburg to New York in a 747. Just as the plane crossed over land in N. America, it pitched savagely downward and became uncontrollable - i could not regain control even with autopilot disconnected. I reloaded the game from a previous saved point, and found it did the same thing in the same position again, although this time i disengaged the AP before i reached that point.

I did check i hadn't run out of fuel and have never been able to explain the cause.

I have also found the AP to be unpredictable at low altitudes. Although i see others here have no problems, i personally feel it is slightly buggy.

Adam