Now, there are exceptions of course, and I imagine that if you were invited to speak at the White House, and showed up with baggy pants and a t-shirt, you would likely be shown the door. It's therefore a good idea to confirm with the host of the event you'll be speaking at, whether there's a specific dress code.
Toss the Turtleneck and Blue Jeans
But what about Steve Jobs with his Levi Jeans and Turtleneck? That might have worked for him, but it certainly won't do for you. Unless you've got the credibility that he had (i.e. reinvented modern geek-free gadgetry or something similar) you'll likely kill your career by coming on stage dressed like a software engineer.
Some sage advice on wearing the right costume...
The following piece of advice is adapted from Carmine Gallo's book "The Presentation Secrets of Steve Jobs". I'm using it because it's spot on:
Great Leaders dress a little better than everyone else. That means that you're smart if you take your dress code just slightly higher than that of everyone else in the room. It also means you don't dress to reflect the current position you hold, but for the leader that you would want to become.
Most hosts and venues won't have strict dress code for speakers and smart casual dress, which has become very common even in white-collar environments since the 1990's, will likely do the job.
But first, what exactly is business casual dress, or smart casual clothing?
While there's no one-size-fits-all generalized definition, it's safe to say, courtesy of Wikipedia, that smart casual dress means dressing professionally, while looking relaxed and yet neat and pulled together. So throw professional, relaxed and neat into on laundry basket and you've got yourself a set of clothing that fits the business casual dress code.
For men, this translates into a collar shirt, without a tie and cotton trousers with neat shoes. Neckties are formal and don't make part of the smart casual code.
For women, a tennis shirt and trousers should work. High-heeled shoes might lean more toward formal, but since many women wear them in any kind of setting, they'll pass for smart casual as well.
Hopefully this gives you some idea of what to wear to a public speaking event. Here are some pictures portraying generally accepted versions of the business casual dress code: