I have a 2002 Honda Accord EX Sedan with manual transmission. I need to replace my tires, but was thinking about upgrading rims from 15" to 16". Is this possible on my car?
The original equipment (OE) are 15" (as you stated). If you look at this TireRack.com page, you'll see they have a selection of wheels ranging from your OE 15" up to 18". As long as you have the correct backspacing on the wheels, you shouldn't have an issue. Sites like TireRack and DiscountTire.com (and others) can help you find wheels which will fit your vehicle. Moving up in size (ie: 15" to 16") is a lot easier than trying to go down in size. Really, you shouldn't have any issues.
There is one thing to check when you move to a different tire size. Check the rotations per mile (or RPM) of the tire and keep it about the same as the OE tires (+/- 1-2% of original). This will ensure your speedometer won't be too wonky when you get your new tires on the car.