Back when the iPhone launched, phonemakers like Motorola were playing it cool, saying they weren’t all that excited about the prospects of touchscreen devices in the United States.

“Historically, carriers and subscribers have been resistant to touchscreens,” Rob Shaddock, chief technology officer of Motorola’s (MOT) mobile devices unit, told CNNMoney.com last March.

Fast forward a few months, and touchscreen phones by LG, HTC and Nokia (NOK) are popping up all over the place. As for Motorola? The Schaumburg, Ill.-based company recently announced it would acquire a 50 percent share in UIQ, which develops mobile operating systems and specializes in touchscreen phones.

“The button-centric experience is transitioning into a touch-centric experience,” says John Wang, chief marketing officer of Taiwan-based HTC, whose keyboard-less Touch phone will be available through Sprint early next month. “At some point, touchphones will become a major category of devices.”

Analysts agree that the range and popularity of touchscreen phones will grow: According to ABI Research, over 100 million handsets with touchscreens will be shipped in 2008. By 2012, that number is expected to reach 500 million.

Next month, Verizon Wireless (VZ) plans to launch the Voyager and the Venus – no, these aren’t code names for NASA projects, they’re phones – both made by LG. Samsung, meanwhile, is expected to soon roll out its F700. By including both a touchscreen and a pull-out QWERTY keyboard in the phone, Samsung hopes to solve one problem many users have with all-touchscreen devices — the lack of tactile feedback.

But almost all touchscreens do at least one thing right: They make it faster and more intuitive to access applications, something that normally takes many clicks and scrolls on a traditional phone.

According to HTC’s Wang, the inspiration for the Touch was not the iPhone (the company says it started working on its all-touchscreen device more than two years ago), but a baby.

“A baby doesn’t look for a small ‘X’ at the top right corner when she’s done playing with something,” says Wang. “We only do that because we’ve been brainwashed by Microsoft to do so.”

Ironically, the Touch runs on Windows Mobile, but the company has simplified the user interface with touchscreen technology. Controls on the Touch mimic human movement, much like the iPhone. Done with an application? Just push it away with a flick of your finger, much like a baby would discard a toy once she’s done playing with it.

More competition for the iPhone will benefit consumers, but Apple (AAPL) might not find the situation so touching.