option exercise
If I buy a call option on March 20, 2009
1.  Strike price of $20
2. Expiration date of May 20, 2009
3. The stock is selling for $35 on May 15

Can I exercise the call option and buy the stock
on May 15 for $35 and resell it immediately?
What fees are involved for doing this?

1) Yes you can.  But you should not consider doing that.  It's simply a bad idea.

2) Most brokers charge a steep fee (more than for buying or selling stock) when you exercise an option (or are assigned an exercise notice.  Of all fees, this one is the most outrageous and I cannot understand how they are allowed to get away with  it.  My broker charges zero. You must ask your broker what they charge, but $15 to $22 is a reasonable expectation.

3) You also must pay a commission to sell the stock.  Total: 2 fees.

4) It's almost always better to simply sell the option when you no longer want to own it.  The broker charges only one commission.

5) Under your scenario, the option is in the money by fifteen points and there is no time premium remaining in the option.  Thus, it's worth $15.00.  If you can sell the option for $15.00, then sell it rather than exercising.  But, if you try to collect $15 and the best bid you can get is much lower (as is sometimes the case when the options trade with very low volume), then you would have to go through the exercise and sell process, as you described.  But, it's easier to sell the call, if you can get a fair price for it.
Mark D. Wolfinger
The Rookie's Guide to Options:
The Beginner's Handbook of Trading Equity Options
Free eBook: