Safelists are sites that have members that agree to accept emails from other members of the site, in return for these members accepting your emails, with the important condition, that no member of the site can or will complain about receiving these messages and report them as SPAM.
Having joined countless thousands of safelist over the years, I can now speak with some practical experience and state the following.
1. You do get some results from safelist advertising. It depends if you are trying to sell something, or give someone a FREE opportunity, such as easy money for answering surveys online. You get a much better clickthrough rate if they are getting something for free, rather than being asked to pay out, however brilliant the item being sold.
2. Most safelists vanish after a while. Hence it is best to join as a free member, and test the waters first.
3. Submitters do increase the number of people you can reach, but most emails get sent to the TRASH automatically before they are seen. At present they are marginally more effective than not sending at all, but only just. Hence it needs huge numbers of potential contacts to get any results. The more you join, the better the absolute number of responses to your emails.
4. Most free email accounts are unsuitable for use with safelists, either they are banned by the safelist, or the safelist emails, including the verification email needed to complete the signup, never get through the email provider's filters. Gmail is not banned so often as Yahoo and Hotmail, but it is more difficult to use and look after. It is also not supposed to be used for junk mailings.
A bit more info is available at
http://www.safe-lists.com, along with some useful links if considering using this method of advertising.