Has it been proven that being exposed to WiFi waves is harmful?
WIFi is non-ionising radiation and so has similar issues to other radiation using similar frequencies such as mobile telephones and microwave ovens. These produce heating effects. WiFi is not focused, so any impact should be very small and perhaps not measurable.
I am not aware of any health studies specifically on WiFi. There have been studies on mobile phones which has shown that while the phone is in use and held next to the head, there is small but measurable heating effect on human tissue. My guess is that it has less impact than standing at right angles to the Sun so one side of the head gets warmer faster than the other. Even then, these studies have produced no evidence that this has any health impact, positive or negative:
The Sun does emit ionising radiation (ultra violet) and that has significant health effects such as sunburn, pigmentation changes and Vitamin D production. WiFi's impact, if anything, is nothing like this.
I am unaware of any research done on this specific question. The closest I've come across was this Dutch study, which states that there may be a connection between Wi-Fi transmissions and tree sickness. The research in itself was not sufficient to make that conclusion.
There are people who report a negative feeling when exposed to Wi-Fi, but those claims don't seem to face a proper double-blind testing, see for example:
Personally, based on my understanding of physics, I doubt that Wi-Fi radiation is harmful. The explanations that fallow are not 100% accurate or bullet-prof, but they should give the general idea.
Wi-Fi transmits at the 2.4 GHz frequency range; that's close to you microwave oven in the kitchen - and it has very much the same effect, that is it heats you up a little bit. Now, while that may be in theory a harmful effect, it should be noted that the change in temperature is much less than due to, say, a having a little warmer weather (I'm cheating a little bit here).
But maybe we should look at it in a different way. This is a nice table from xkcd:
While admittedly not the most solid source of information, I do believe it can give the general notion. Look at the lowest dose of radiation that any research ever found to be linked with cancer (100 mSv), and compare how much radiation you are exposed to on your daily life.
The difference is quite large. So even with the (rather small) addition of radiation from Wi-Fi, you should be fine.
I did find one study about WiFi and trees. Conclusion translated to English from Dutch:
Also per this study by the California Department of Health Studies -- be advised, this is about EMFs from power lines, and I'm not clear how much stronger / weaker those are compared to radio frequency EMFs from cell phones and wifi:
As you can see from the "degree of certainty" from these professionals, the jury is very much out on this one.
In my opinion in the absence of even mildly compelling proof of danger, I don't think there is harm from reasonable, typical exposure to WiFi.
Yes, an increasing body of research links WIFI with cancer and other harmful effects. Here is a study from 2013 dec that involved plant seeds:
Also, a recent israeli study linked cell phone use with an increased presence of free radicals in saliva!
One more quote for the downvoters from a recent event :D