Ooh! Interesting question! I'm going to have to google this one.
googling, googling, googling
Okay! The answer I found: Kind of. They can help, but they won't completely solve the problem of either allergies or odor and some are definitely more effective than others.
Allergies: You'll still need to clean your floors and surfaces to remove dust and account for the fact that some allergens like pollen are too heavy to float for long.
Odor: They'll definitely help when they're loaded with several pound of new carbon, but this will lose effectiveness over time so you'll have to stay on top of replacing it.
Best Bets: "Of the ones they recommend, the IQAir HealthPro Plus air purifier garners the most accolades for the best all around air purifier. The Airfree Sterilizer is recommended for virus capture and the Airpura T600 Smoke air purifier is recommended for the removal of smoke and its associated odors." - http://www.allergyconsumerreview.com/do-air-purifiers-really-work.html
Keep In Mind: "One of the major problems associated with air purifiers is the production of a heavy oxygen gas known as ozone. Ozone in the atmosphere serves as a protective layer against harmful solar radiation, but concentrated ozone in a confined space can cause a number of serious health problems. Many air purifiers using electrically-charged plates do generate ozone as part of their process. The health benefits of purified air may not be enough to overcome the potentially harmful effects of ozone-producing air purifiers. Consumers should look for HEPA filtration, low ozone production and some form of air circulation when shopping for air purifiers. The passive electrostatic air purifiers may offer some piece of mind, but very little actual health benefit." - http://www.wisegeek.com/do-air-purifiers-really-work.htm#