From Daily Wireless:
In one of the largest studies into the short-term health effects of mobile phone technology, just completed in England (pdf), Essex University measured “heart rate, blood pressure, and skin conductance,” for reactions over three years. The research study all but debunkes the theory that cell phone towers, or electronic interference, is making people physically ill, reports the BBC.

Britain’s Health Protection Agency (HPA) said that they could find no scientific evidence that feelings of anxiety, nausea, and tiredness occur due to the presence of electronics, or GSM and 3G cell phone equipment or WiFi.

The Key Points in their finding:
There is no consistent evidence to date that exposure to RF signals from WiFi and WLANs adversely affect the health of the general population.
The signals from WiFi are very low power, typically 0.1 watt (100 milliwatts) in both the computer and the mast (or router) and resulting exposures should be well within internationally accepted guidelines.
The frequencies used are broadly the same as those from other RF applications such as FM radio, TV and mobile phones.
Based on current knowledge, RF exposures from WiFi are likely to be lower than those from mobile phones.
On the basis of current scientific information, exposures from WiFi equipment satisfy international guidelines. There is no consistent evidence of health effects from RF exposures below guideline levels and no reason why schools and others should not use WiFi equipment.

Summary: On the basis of current evidence, the HPA does not consider there to be a problem with the safety of WLAN.