Happy PayPal'ing. Really depends on whether you're sending or receiving.
Outside of the obvious scam/phishing nonsense that you'll see through your email, the thing with PayPal where I think you need to be legitimately concerned is if you are accepting PP as a method of payment where customers will pay you for goods/services. The 'common' scam is for a buyer to buy a high-ticket item, pay you through PayPal by using their credit card, then stopping pay and issuing a charge back after you've shipped.
What will happen is PayPal will grant the charge back and wipe out your account w/ the refund, and you've already shipped the item, so you're basically hosed with nothing but a recipient address. If you are actively buying/selling goods like a lot of eBay-junkies do and have already reduced that balance, then PayPal may dip into your 'real' brick-and-mortar bank checking account to cover the difference, which you will have authorized them to do if you've linked it as a backup funding source. The implication behind that is now you might wind up having checks floating in circulation that overdraw your account.
It's really just a lot of common sense stuff with being careful and smart about it ... managing your money well and all that jazz.
I suggest people set up their PP account, link the bank info and confirm your address, transfer in some money or sell a few things on eBay to jumpstart building money in the account, then unlink any 'real' bank account info or credit cards as backup funding sources. Another option is to create two accounts, using one to move money to/from your bank, then transferring it PayPal-to-PayPal into another PP ID for the transactions you do anonymously. You'll lose some money on transaction fees, but that's a small price to pay to have a buffer between Joe Schmoe on the Internet and that honey pot right in front of your real bank/credit card account in the form of a directly linked PayPal ID.
Don't carry a balance in your PayPal that you can't afford to "lose," whether by abuse, neglect, fraud, or even a mistake on PayPal's part. Remember, PayPal is not a bank and is not FDIC insured. You are using them as a wireless money transfer service in good faith.
If you do a lot of business by PayPal, opt in for a PayPal Debit MasterCard. Pays cash back into your PayPal and can be used for credit/debit/ATM with a limit of either $3000 or your full PP balance, whichever is lower.
e.g. I sell on eBay, get paid into PayPal, then pay my USPS shipping charges and eBay fees with my PayPal MasterCard, which winds up returning a couple bucks right back into my PP account due to the cash back bonus. The cash back incentives really offset the per transaction fees, so I'm not losing a dollar or three everytime I sell something online.