How to know if you really need an agent
An actor doesn't technically 'need' an agent, but it can be incredibly hard to find any work without one, it's hard enough if you DO have one! The industry works on trust and reputation, so if an agent represents you, it tells the casting director that someone else has faith in you and your abilities. Therefore, you have a better chance of being seen for the job. Of course agents have status and reputations too, so some agents will be more trusted by casting directors than others.
The plus side of working with an agent, especially if it's a big one, is that you are more likely to be auditioned for jobs and the jobs that you are auditioned for will tend to be of a higher quality, getting you more exposure and crucially, paying you more. They should also handle the legal side of things and make sure that you are paid and treated fairly.
The negative side is that you have to give the agent a percentage of your earnings, regardless of whether or not they found you the audition in the first place. Also, with some of the bigger agents, they might ask you not to do lower paid work or work that ties you up for a long time, in favour of leaving you available for possible better paid work that could come along. Of course, the issue there is that the better paid work might never come.
If you can't secure an agent or decide against working with one there are still things you can do to find work, there are a lot of casting websites out there but you can also help yourself by doing a lot of research and writing a lot of letters and e-mails. Check theatres and theatre companies websites and contact them to find out how they handle castings. Sign up to their newsletters and when you see them advertise something that you might be suitable for get in touch.
It's tougher to find information on film and t.v work, but if you check online for films in pre production you can find out what is coming up, and check the production company's website for further information.
The bottom line is that you don't need an agent, but if you don't have one then you need to be prepared to work very hard to find work for yourself.