For practical purposes, I would strongly suggest that you do create a separate account for each business you may have that is used only for business purposes, and use it for all of your business income and expenses. This will allow you to get an accurate picture of whether you are making money or not, what your full expenses really are, how much of your personal money you have put into the business, and is an easy way to keep business taxes separate.
You will also be able to get a fairly quick read on what your profits are without doing much accounting by looking at the account balance less future taxes and expenses, and less any personal money you've put into the account.
Check out this thread from Paypal about setting up a "child" account that is linked to your personal account and can be set up to autosweep payments into your main account, should you like. You will still be able to see transactions for each child account.
NOTE: Do be careful to make sure you are reserving the proper amount out of any profits your startup may have for taxes - you don't want to mix this with personal money and then later find out that you owe taxes and have to scramble to come up with the money if you have already spent it This is one of the main reasons to segregate your startup's revenues and profits in the business account.
For those using "brick and mortar" banking services rather than a service like Paypal:
You likely do not need a business checking account if you are a startup. Most likely, you can simply open a second personal account with your bank in your name, and name it "John Doe DBA Company Name" (DBA = Doing Business As). This way, you can pay expenses and accept payments in the name of your startup. Check with your banker for additional details (localized information).