Olympus E-P2 Flash
To the disappointment of some, the Olympus E-P1 didn't have a built-in flash, and the E-P2 continues that omission. It does, however, have a dedicated hot shoe for mounting external flash units, like Olympus's compact FL-14 flash. Other Olympus flash units such as the FL-50R, FL-36R and FL-20 also work, and non-dedicated units can also be used provided they have a compatible trigger voltage and polarity. (Olympus hasn't stated the trigger voltage or polarity, though.)
Note though that the hot-shoe offers photographers an either/or decision: if you want to use the shoe-mounted external electronic viewfinder or external mic input adapter, then the hot shoe isn't available for use with an external flash strobe. Given that the P2 doesn't offer a sync terminal or wireless flash support, this means you have a decision to make for any given shot -- do you want flash, or do you want to use the accessories? Using both at once isn't an option.
The advantages of a good external flash are many: more power for increased range, faster recycle times, longer battery life, reduced red-eye, auto zoom to match coverage to the current focal length, and the ability to adjust the tilt and swivel of the head to allow light from the flash to be bounced off nearby surfaces such as a ceiling, for a diffuse effect. (The FL-14 does not, however, tilt for bounce-flash operation.) Many external flash units have a powerful AF assist illuminator, and other useful features such as modeling flash and high-speed focal plane (FP) sync mode are common on higher end models.
When using a dedicated external flash with the Olympus E-P2, seven flash modes are available: Auto, Red-eye Reduction, Forced On (Fill flash), Forced Off, Red-eye Reduction + Slow Sync, Slow Sync, and Slow Sync 2nd Curtain. X-Sync speed (the maximum shutter speed with the flash enabled) is 1/180 second by default, about average these days. Through a Custom menu setting, this upper limit can be reduced in 1/3 EV steps to a minimum of 1/60 second. A separate Custom menu option allows configuration of the minimum shutter speed at which an attached flash will fire. The default is 1/60 second, and can be altered in 1/3 EV steps, within a range of 1/30 to 1/180 second. The high-speed FP mode offered on some external flash units including the FL-36R and FL-50R is also supported, which should permit flash usage up to the 1/4,000 second maximum shutter speed the E-P2 is capable of.
The Olympus E-P2 allows you to adjust flash and ambient exposure independently of each other, by providing flash exposure compensation between -3 and +3 EV in one-third EV increments. An option in the Custom menu also allows for flash exposure compensation to be independent or additive to ambient exposure compensation. Flash exposure bracketing is also supported, where three shots can be taken at one-third, two-thirds, or one EV increments of flash exposure compensation. The metered exposure is captured first, followed by shots under and over the metered exposure, each with a separate press of the shutter button. Of course, if the external flash supports it, manual output power control is also available.