LLC's are required to appoint an agent to accept service of process, which (in MA) may be an individual resident, or a domestic or foreign business entity. Some attorneys like to serve in this role to maintain an active relationship with their client and to be able to be a fast responder in the event litigation is served. Some prefer to appoint a commercial third party provider (such as CT or CSC) to provide for long-term continuity and the ability to designate a specific recipient so important process or tax notices aren't floating desk to desk looking for the right home.
In MA and some other states, the Registered Agent is required to consent to the appointment and some states even require the physical signature of the appointee. As Brendan says, an Agent's failure that results in a default judgment could perhaps not only open up an Agent to litigation, but perhaps trigger a malpractice claim if the Agent is an attorney, although Registered Agents will generally accept no liability where a company failed to update them with address/contact changes. Generally, the failure to forward annual report or tax notices that result in forfeiture/delinquency can be easily cured by catching up filings and paying late fees. It's interesting to me that in 20+ years as a paralegal, I've never heard of litigation against a Registered Agent. (And don't litigants usually serve multiple ways - on the Agent and via mail and personal service to the principal business address? Litigation is not my specialty, but maybe the possibility of an Agent causing a default judgment or sufficient damages to warrant litigation against them are slim in any event).
The purpose of a registered agent is to serve as the physical representative of the LLC. This allows individuals/other entities to deliver important legal documents to the LLC. Examples would be notice of a lawsuit or notification by a creditor that the LLC is in default. As the name limited liability company implies directors, officers, agents, and employees of the company (except for rare circumstances) are not personally liable for claims against the company. This includes the registered agent.
The situation in which a registered agent could expose him/herself to liability is when he/she fails to meet her responsibilities. An example is when the registered agent fails to notify the company they are being sued and this results in a default judgement against the company. In this situation the registered agent was negligent in fulfilling its duties. It is also likely the LLC has a contract with the agent. Failure to notify the LLC would represent a breach of the agreement.
To add on to the previous 'answers', there are two articles I encourage you to review regarding Registered Agents. One provides a definition of Registered Agents: http://www.toolkit.com/small_business_guide/sbg.aspx?nid=P01_4769 and one helps explain why a commpany may choose a third-party provider to serve as Registered Agent: http://www.bizfilings.com/learn/10-reasons-registered-agent.aspx.