Dawn,
Yes, an acceleration provision typically means that the stock options will fully vest in the event of a takeover (most commonly, because employees are concerned that the new firm may fire the old staff and thus cause the option value to be lost). Of course, whether the options actually have value or not (i.e., whether the stock price is high enough for them to be worth something) is another matter!

As for what typically happens to the value of a company's stock after it is bought it, the answer is that it really depends on the deal and the situation. In some cases, the company is bought for cash - which means all of the stock is sold at the agreed-upon price, and after that it's up to you to reinvest your proceeds! In other cases, the shareholders in the original firm may receive stock in the new firm - which means you're subject to the vicissitudes of the new company's stock (in the same way you were with the old company's stock), and it's really a matter of the financial outlook for the new company.

I hope that helps a little!

Where there is an "acceleration provision," does that mean that the options would automatically become vested in the event of a takeover, and the employee could exercise them immediately if he chose?

Also, what typically happens to the value of a company's stock after it is bought out?

Vanessa,
As far as I know, there is not necessarily any up-front legal requirement for a buyer to honor stock options of the acquired firm.

HOWEVER, from a practical perspective, they are virtually ALWAYS honored. This is true both because the original firm's stock option agreement will typically have acceleration provisions that provide the value of the options (and often fully vest any not-yet-vested options) in the event of a takeover, and also because the buying firm nearly always agrees to fully honor the commitments of the preceding firm. The reason is relatively straightforward - if the employee fears a takeover and that the options will not retain their value through a takeover, the employee is demotivated, and may leave for a competitor. So it's in the original firm's interests to secure the compensation of their key employees to retain them. And it's in the acquiring firm's interests (at least in most cases) to likewise secure the compensation of key employees, otherwise you end out buying a firm and getting none of the talent that got the firm where it is!

I hope that helps a little!