And then there is the dreaded X - the one that invites you to close the ad yet seems impervious to repeated clicks of the cursor or the jabs and thrusts of even the most powerful fingers. (Perhaps you have tried a hammer?)
Sometimes the ads dance and move across the screen, forcing the user into a hot pursuit of the X.
"How many times have you hit the X and it doesn't work?" said Tony Weisman, the chief executive of the digital agency DigitasLBi North America. "Now it's just a cruel joke."
Online advertisers and consumers have tried to outmanoeuvre each other since the early days of the web - with sellers continually finding ways to prolong engagement with ads and users trying equally hard to avoid them. But the cat-and-mouse game has reached a critical point, especially as devices have gotten smaller: ads have become so annoying, consumers and industry executives say, that they could sink the Internet if they were not also helping support it.
"Ads are getting more pervasive and more difficult to easily get past," Mr. Weisman said. "We are just destroying the user experience."
On desktop computers, ads have turned web pages into mazes. A recent visit to Salon.com, for example, meant fending off expanding banner ads and navigating video ads that played automatically. Sponsored posts and animated display ads filled each page.
On tablets and smartphones, the problem is more acute. Ads dominate the smaller screens, and many ads are not formatted correctly because of out-of-date technical language. The X button can be so tiny that clicking it requires a fair amount of luck. Industry executives often cite a 2012 report that said up to 50 per cent of advertising clicks on mobile were accidental.
Annoying ads have become problematic for Anthony Martin, a 32-year-old consultant for a project management firm who sat in Bryant Park on a recent Monday afternoon, iPhone6 in hand. He had moved to New York not long ago, he said, and was using a smartphone app to determine the best subway routes. But as soon as the app loads, ads take over his screen - first a banner ad on the bottom, then a full-screen ad. No amount of desperate jabbing does the trick.
"Sometimes I miss a stop," he said. "Especially with fat fingers."
Industry executives say it is quite likely that publishers and mobile developers are deliberately building ads that are hard to escape or shut down.
"The ones that are incredibly invasive are designed to be that way," said Brian Gleason, the global chief executive of Xaxis, a media and technology company owned by the advertising giant WPP.
Mike Pilawski, vice president for product at Vungle, which builds and serves mobile video ads, says some advertisers ask Vungle to make the whole screen clickable at the end of the ad - not just the X or other specific buttons - which would make the ad difficult to close. He says Vungle refuses to do that, but it does design ads with X buttons in the top left instead of the usual top right. The switch confounds some users, though he insists that is not the intent.
Bad web ads have deep roots. According to Ethan Zuckerman, who helped invent the pop-up ad in the 1990s, those behind the early Internet turned to advertising out of necessity.
"There were so few people online, and the Internet was so new, and everybody still thought it was a fad," he said. "It would have been hard to convince anybody to put money down."
Pop-up ads were intended to give advertisers a way to separate their message from the web page. (This became especially important, Mr. Zuckerman's story goes, when a car company became upset after it bought a banner ad on a page about anal sex.)
Advertisers soon began tracking web users and serving them targeted ads. Later, companies like Rocket Fuel and Rubicon Project started selling technologies that automated this process, which eventually helped decrease the price of online ads.
But cheap online ads squeezed publishers, who responded by cramming more aggressive ad formats onto their sites to secure enough revenue to stay alive.
During this time, the technical language that publishers used to build their sites became more advanced, allowing them to design highly creative, interactive ad formats far beyond flashing banner ads and static pop-up windows. Many publishers have shifted to HTML5, which helps them create new ad formats.
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