Off the cuff, dye sublimation would be my first answer, but that's not very thorough of an answer because there are different substrates for different uses, and each has its own special ink set.
For instance, if you need a polyethylene OSHA warning sign, you are not going to be using dye sublimation. You'll either screen print or use a flatbed digital printer, most likely an inkjet printer that uses liquid solvent inks. If you need a lot of signs, screen printing will probably be the most cost-effective method, unless it is a 4 color process print.
Vinyl Decals and Graphics
Vinyl decals and graphics are another item that has a few options for imprinting, including thermal dye sublimation, although it is only good for very small orders as it's quite expensive compared to screen or digital inkjet printing.
Nylon or Cotton
How about fabrics like nylon or cotton? Screen-printing is generally considered the best option, although different inks are used on nylon than on cotton or other fabrics generally used for shirts and such.
However, for sheer printing beauty, when required, there is nothing, in my opinion, that touches dye sublimation on fabric banners, posters, or displays. The continuous tone printing cannot, at this time, be matched by any other method.
Dye Sublimation Printing
Continuous tone printing is accomplished with the dye sublimation process. Using the CMYO (cyan magenta yellow overprint clear), the dye is printed on a transfer paper. Then once the paper is printed, it is matched up to whichever fabric the client has ordered - banner, oxford, satin, outdoor, stretch - and sent through heated rollers at about 400F.
As the fabric and transfer paper go through this heat/pressure combination, the dye printed on the paper is converted from a solid to a gas instantaneously, and is fused to the fabric in a continuous tone print, similar to a photograph.
The difference between most printing and dye sublimation fabric printing is that most, including screen printing, and all types of digital printing, use a dot pattern to create color, whereas dye sublimation cloth printing has a continuous tone, just like pictures that you get developed from your camera.
So, I guess that means that my first answer is correct, at least for fabric imprinting. The other substrates are good for certain things, but for the classiest look, you will want to definitely consider dye sub fabric printing.
One other plug for dye sublimation printed displays - if you are at a competitive trade show, or similar, and your competitors have some nice graphics on vinyl or the like, and you show up with your continuous tone printed fabric display, you are going to win the subliminal war. Face it, if your display looks rich, and theirs looks middle-class, they'll get some clients, maybe lots, but you'll land the best clients at better margins.
ABOUT THE AUTHOR
Barry Brown has been in the Sign, Banner, Decal and Display Business for over 20 years. It isn't what he thought he'd do with his life, but he says he knows too much now to do anything else!
He has been marketing these products online since 1998, and the company he was general manager of in 1998 was the first sign company to be listed on Yahoo!
You can check out and follow him on Flickr to see the graphic print displays he does.