You can put ™ on anything; it simply means that you consider it to be a trademark for your product or service. The registered trademark ® is used to indicate that your trademark is registered with the government, which gives you a wider range of statutory remedies in case of infringement. You only use the registered bug if you've actually registered the trademark formally, but you can use ™ freely.
For services (as opposed to products) you can use SM instead of TM.
In the U.S., you must first use the trademark regularly to establish it as such, then you can register it. No longer true, thanks to /u/LWRellim and /u/Throtex for pointing it out.
In other, more class-conscious societies, such as some European countries, you can register the trademark even before you've actually proved that it's associated with your product or service.
The copyright bug © can be used with any copyrighted material, registered or not. Unlike trademarks, copyrights exist as soon as something is created, so you can use this symbol freely for anything you create that is covered by copyright (books, songs, music, images, etc.).
Under Windows, the registered trademark bug is Alt-0174, the copyright bug is Alt-0169, and the TM bug is Alt-0153.