I have a question which seems simple, but I keep getting different answers from people I talk to.

That usually means the question really isn't that simple. Or you are talking to people who aren't well-informed on the issue. Or both.

If I exercise stock options and hold the shares, am I responsible for taxes on the difference between the strike price and the market value at the time I exercise them? (One person I talked to said it depends on whether I pay the Alternative Minimum Tax.)

It depends on the type of option. Incentive Stock Options are not taxable at exercise for regular tax purposes, but they are for AMT. Most other options are taxable at exercise. And the length of time you wait between the exercise/hold and the ultimate sale will also have an impact.

www.fairmark.com has some excellent resources regarding stock options.

--Peter