In general, the quick answer is NO.
However, there are some boards that were designed to take either kind. I know of at least one that was made by Gigabyte. That said, those were all older boards that were released during the time of the industry switch from DDR2 to DDR3. Most boards made today are designed to take DDR3, although you can still find Intel boards using the 9xx series and G4x series chipsets that take DDR2.
While DDR2 and DDR3 both have the same number of pins (240), as "anort3" said, they are keyed differently.
In the end, unless your motherboard clearly states it can accept DDR3, then it's almost assured that it cannot!