The ™ symbol, which stands for "trademark," and the ® symbol, which stands for "registered trademark," are often overused or used improperly. For one thing, they are not interchangeable. (Actually, the ™ can be used in place of ®, but that defeats the purpose or registration. However, the ® cannot be used in the place of ™ if the trademark is not registered.)
By definition, a trademark is a unique name, symbol, phrase, motto, or graphic design that is specific to a company name, or its products and services.
™ simply "warns" that the mark or words are the trademark used to identity the brand or product. ® designates that the trademark is registered by the patent office. This provides a strong case against infringement. You can read up on that in this pdf from the USPTO.
In many cases the branding is so obvious (as in a highly customized logo) that the placement of the ™ symbol is truly unnecessary, and in many cases distracting from the design of the logo. Too often it is even included when the logo is reproduced very small, especially on a web page, and the ™ looks like a speck of dust or errant pixels. That is when it definitely should not appear.
Also, it is not necessary for the symbol is to appear in every instance of the trademark in a brochure, ad, website page, and so on. Just once, in the very first instance as on the front page, is all that's necessary. Even then, if it distracts from the design, move the ™ or ® to the next instance of the logo's appearance. It is in bad taste to include either symbol on the logo of a "showcase" piece, such as the business card.
The ™ is helpful, however, to convey ownership of a word or phrase that is the product name, company name, tagline, or marketing phrase, when such is set in plain type in the body text of an article or ad. The ™ is, more than anything, used to suggest exclusive use and "scare off" anyone from applying the word(s) to their own business. Unless the word or phrase is registered, however, there may be a dispute as to whether it can be used by others.
Another useful place for the ™ symbol is next to a logotype (an identification mark made up of letters only, such as Panasonic) that is not obviously, due to its plain font look (even if the letters have been modified by the designer), the "official logo" for a company or product. Then it's a good idea to place the ™ next to the logotype, at least once in each marketing piece.
Placement of the ™ is traditionally at the upper right corner of the logo or logotype, whereas the ® is traditionally placed at the lower right. Rather than simply setting the ™ or ® as superscript on a logotype, I always select a plain font in a light face and a small size that complements the style of the trademark.