Yes. Waves plugins have this: http://www.waves.com/Content.aspx?id=244
Ive used it a few times and it sounds ok but it is not free however.
Also Cakewalk sell this: http://www.store.cakewalk.com/b2cus/ProductInfo.aspx?productid=36-CWSF3.31-10E and it has a doppler as part of the surround package.
Some free ones:
http://laut8leise.de/_l8l/asa.html (called "away" but you may need to change the file extension to .iso for it to work in windows - http://www.fileinfo.com/extension/toast)
http://www.kvraudio.com/product/spacestation_by_oli_larkin - seems to be unavailable but his website is still up http://www.olilarkin.co.uk/
A basic replication could probably be achieved however with some pitch and volume automation.
Taken from : http://forum.cockos.com/archive/index.php/t-106794.html
"Use pitch-shift and automate the envelope to have a tangential profile. Ie start with the sound pitched up a couple of semitones and over the period of time gradually start to drop the pitch, have the envelope slope at its steepest as it crosses pitch neutral, and then gradually bottom the slope out at 2 semitones pitched dowm. 2 semitones is a starting point, depends on relative velocities...
If you follow a tangential shape for the pitch envelope, this will mimic the rate of change of source relative velocity and the resultant pitch change experienced by an observer being passed by a constant velocity sound source.
The maths isn't that complicated if you had real numbers to play with, but it should follow a tangent function of variable positive and negative start and end pitches, with a zero-crossing angle dependent on how close you would be to the moving object (nearly vertical for fast and close, more gentle for slower or further away).
Everything else is level, noise and timbre -add some rumble, white noise and filters and and volume envelope the lot of them ;)
Have fun! :D