Since there is no official way to look up cell phone numbers, you can be in quite a pickle in a hurry. The privacy laws and the sectors of the industry keep this from happening. This does not mean, however, that private companies have not risen to the challenge of providing a service. There are companies that have compiled mass searchable databases which are specific to cell phones.
The problem with these directories is that many times the owner of the number is not known. Wireless phones do not have caller ID and normally only numbers in the owner's contact list can be identified. Now there are incoming calls and missed calls which can not be identified. Many people would rather them remain this way than to call back not knowing what to expect.
The reverse cell phone lookup was developed to change all that. A reverse cell phone directory lets a user take a cell phone number and find out the owner's first and last name, state registered, (sometimes) the address, and who the service provider is. Many of these services are offered at a fee. The fee is modest in many cases, but you can not be sure of what you are buying up front.
It would be wise to use a search engine to find reviews and consumer sites that reference the service prior to dishing out money. Review the reverse cell search site's policy as well. Many do not provide a return of funds if no results are found.
These services are completely legal as long as the information is not used to perform telemarketing.