I'm currently looking at flights for two holidays later this year with two popular budget airlines and I've just done the private/normal browsing trick.
There is no difference in price and one set of flights where I've looked a few times (prices have been up and down all over the place) are currently cheaper (even on normal browsing) than I've seen them in the last few months so I've booked them. They could go up or down further from now on, but at least we've now secured our flights.
I'm not saying it doesn't happen, but I've never noticed it. I often search in one browser and book in another because I use quidco as you often get a few quid in cashback and they say clear your cookies to get the cashback (if you search through expedia for example, the cookies will direct the cashback as commision to expedia as that is how they make their money). So search in one browser and book in another as the cookies are tied to the browser if you see evidence that it is happening.
However, I have noticed very different pricing when looking via different routes when looking for travel insurance - the price you get through a comparison site will be different to going direct. Similarly hotels - different comparison sites show different prices - I think this is the point of the hotelscombined website.
In my experience, the price of flights for us never varies that much for the type that we book (DP and I fly to Europe approx 4 times per year, outside school holidays). Probably varies by less than £100 for the two of us, which is about 10% or less of the total cost of the holiday. While it's nice to make a saving, its not worth getting into a huge tizz over.
I know of someone whose job is to set the pricing at a budget airline. It is a hugely complicated art with lots of variables but the aim is to fill the plane with people paying an average price that is as high as possible, purchasing as many extras as possible. Empty seats lose them money, as do too many discount seats. But if they don't discount the seats, people will go elsewhere if there is a choice to do so. He has a fancy title that is something like 'Revenue maximisation executive'.