While manning the booth and touring the show floor at CES, I decided to wear my iPad an a case from a company called modulR, with a neckstrap. The result was an electronic "sandwich board" that got a lot of attention. Everyone kept asking me where I got it. Even the Modulr wasn't officially at CES, they got a lot of attention as well!
If you want to try the same thing with an iPhone, several vendors offered some interesting solutions. iHold Technologies makes cases for the iPhone 4/3G/3GS in black, white, smoke, or clear colors. The cases have a fold out clip that allows you to attach the included neckstrap. Those neckstraps are available in a wide variety of patterns, as well.
Another option for hanging an iPhone, or just about any phone for that matter, is Allsop's Clingo universal mobile neklit. Allsop's distinctive line of Clingo products stick to an iPhone and most devices with a flat surface. The neklit has a neckstrap so you can "stick" your phone on the Clingo surface and wear your phone around your neck. You can even run a clock app and pretend to be Flavor Flav!
Suppose you want to keep your iPad close at hand but not around your neck. Handeholder has a handgrip that secures to the iPad using essentially an industrial grade velcro style attachment. They even have a leg/thigh attachment which is favored by pilots who need their iPad close but also need their hands free.
Finally, if you're not ready to wear your technology on your sleeve, so to speak, Tunewear was showing more traditional ways to strap your gear on you in a more subtle manner. Their Tunefolio Urban for iPad is available in vertical ("tall") and horizontal ("wide") formats. Like other iPad cases, it looks like a traditional portfolio but they wisely added shoulder straps so you can wear your iPad over the shoulder or like a messenger bag. The Tunefolio is available in white or black as well as orange if you decide you do indeed want to draw attention! They also offer the "Strapocket" and "Xtrapocket" which allow you to clip your phone to your existing luggage, purse, etc.