Depends on what for.
From the FAA's standpoint, you can certainly rent an airplane to fly you and your friend to the Superbowl and share costs or even to use it for local air tours, pipeline patrol, and any of the other things a commercial pilot can do without there being an operating certificate under 119.1.
The rental issue comes into play with something the FAA calls "operational control."
If a Peter Passenger owns an airplane and pays you to fly him around, all you are being paid for is piloting. You're not considered to be in charge of the operation (now there's a bad word in the FAR - the meaning of "operator" really does morph with the context). And no operator certificate is required because the the owner/passenger has "operational control" meaning that, except for the flight safety-related issues that come with being PIC, it's the owner that decides what the airplane is used for, where it goes, and when. You're really just a paid pilot and nothing more.
But if you, the pilot, own the airplane, you have "operational control" and the passenger becomes "carriage" - a no-no if you're receiving compensation unless you fit into 119.1, 61.113 or some other reg.
The rental issue is this - clearly, if the pilot rents the airplane, the pilot has "operational control" while the airplane is in his possession and control for the term of the rental.
But what if the passenger rents it?
Then the question is whether the rental looks, smells or quacks like the passenger or the pilot really is the one with operational control. And the FAA is going to look real close. For just one question, is that FBO really transferring responsibility for the airplane (operational control) to a non-pilot guy off the street or to the pilot who has met the FBO's checkout qualifications?
That's why rentals are problematic - it's going to be the rare rental that really qualifies as a transfer of operational control to the passenger, not to the pilot.
Getting a headache yet? You should be. The operational control issue gives headaches to lawyers who work with it in the context of aircraft leasing and setting up business flight departments.