I have worked 5 years with the same company and received a w2. The company was taken over by another company. My last day as an employee was 1/31/13. The current company asked me to stay on for 2 months to help with the transition. I will receive a 1099. Will I be able to apply for unemployment benefits when my contract ends? Should I apply now? This is in NY.

You would be collecting not on your 1099 work history.. as a self employed individual you would not qualify... however you COULD apply based on your previous 5 year work history where you weren't technically self employed..

Given that you have another month of contract work, I would go talk to the Unemployment Office about applying now or then. I have a feeling that they will say then. But apply the very day you stop working.
Assuming that you were properly laid off, you can collect from the next day. I'm not positive about what happens when you are hired to stay on as a contractor. Strictly speaking, it wasn't an IRS legal arrangement. You don't qualify as a contractor, working on their premises, and with no other income, and no insurance of your own. Those are just 3 of many requirements for them to pay you that way.

You should be able to qualify for UI benefits. However you will be required to report any contract work for which you receive income in each pay period. In other words, you would get reduced UI benefits.

As Joy indicates, 1099 "independent contractor" is frequently a ploy on the part of an employer to evade employment taxes. If you are not actually an "independent contractor", your employer can, in theory, get in trouble for tax evasion. That wouldn't be your concern, however, in my opinion.