I have been offered another job, and I would be crazy to turn it down. That being said, I have been at my current job almost 7 years. I am conflicted about when to turn my two week notice in, technically two weeks from today is my anniversary at my current job. On that 7 year anniversary, I will accrue 15 vacation days, this would be in addition to the 9 days I currently have. Should I expect to be paid for those days? I have read our "handbook" and it doesn't touch on this topic. I have enjoyed my time here and don't want to cause any drama, but I have also been an asset to the organization and I feel I am due my benefits.
You need to clarify with your own HR department what their vacation policy is, and how they account for vacation time accrual.
Depending on where you live, the word accrue is important. In many states in the US, if you have actually accrued vacation time (it has been credited to you in the company's accounting system), it is considered compensation that must be paid to you. If you are merely eligible to begin accruing vacation time, but have not yet accrued it, then they are not obligated to pay it to you.
Most companies with vacation day policies accrue your full yearly allotment over the course of the year (e.g., 1/12 of your eligible time each month), allowing you to spend days you haven't technically earned (accrued) yet, based on the fact that you'll accrue them as you work for the rest of the year. If you leave the job having spent more days than you've accrued, the company is within its rights to withhold the deficit from your final paycheck. Some do exercise that right. Others simply forgive it and move on.
EDIT: As @Blam states in the comments below, the federal Fair Labor Standards Act does not address time-off policies, leaving it to individual states. Most states also leave it to the companies to decide. But where the states can step in is under their laws governing contracts. If there is an employment contract stating actual accrual of time-off pay, then you have a good reason to believe they will pay out unused time-off pay. At any rate, don't assume you have the days off until you see them on your pay stub. The easiest way to know for sure is to ask your HR department.