If you're editing and aren't logged in, you're in some sense a second-class citizen on the site. Expect less tolerance of minor infractions of policy and guidelines. That being said, everyone editing from an account should be treated equally, as an editor. Although editors hold different titles on the site, no one has any actual added authority when it comes to saying what should and should not be in an article.
In particular, the site administrators (or sysops) are not supposed to use their greater technical capabilities to exert influence on content. This is a basic point but one that is easily and often misunderstood. Administrators are usually experienced editors, who will naturally know the system better and will probably be more adept at managing discussions about policy and its application. This doesn't mean that what an experienced editor has to say trumps what a complete newcomer has to offer. From its outset Wikipedia has tried to get by with a very flat user structure, without a hierarchy of editors, and in contributions to articles that ideal persists. Wikipedia does have, however, a small variety of account types with different technical privileges, which are detailed next.
The majority of tasks on Wikipedia can be performed by anyone, whether that person is logged in or not. A handful of user access levels are defined, with progressively broader privileges; these are detailed in full at [[Wikipedia:User access levels]]. Note that these are functional distinctions, not an indication of the editor's importance on the site or the role he or she takes in contributing to content. [[Category:Wikipedia functionaries]] provides some categorization of individuals with particular roles on the site, which may not be related to Wikipedia access level.
The other status classes are listed below for reference. Very few editors, relatively speaking, fall into these classes.
Administrators, often known as sysops (for system operator) or just admins and sometimes referred to as janitors, are editors whose editing privileges have been increased. Ambitious to become one? You'd better know what's involved. The janitor nickname is in place for a reason. Administrators have little extra formal power in making editorial or policy decisions. Instead, they tend to do very messy cleanup work, revert vandalism, keep an eye on Recent Changes, watch out for disruptive users, and delete junk pages.
Administrator powers are given to editors who have proven themselves to be experienced and trustworthy though a process called Requests for Adminship (RfA). Adminship was originally designed as a temporary measure to reduce vandalism on the main page; as the community grew, it became a useful way to grant extra privileges to experienced users so they could do needed work.
So what are their superpowers? Admins can block disruptive editors or IP addresses from editing. This not done lightly, and doing it to gain editing advantages would cause a scandal. This power requires a proper understanding of site policies and customs.
Furthermore, admins are able to delete pages from public view, and they can view the histories of deleted pages. They are also able to delete uploaded files, edit protected pages (such as the main page) and protect and unprotect pages. They can protect pages from being moved (or move a protected page) and edit pages in the MediaWiki namespace, which changes the look and feel of the site. There are formal processes for doing most of these things, including blocking, deletions, and making interface changes, which admins are expected to follow. Admins are accountable for their actions and should respond reasonably when their use of power is calmly questioned.
Adminship is a duty, not a prize. The only reason to become an administrator is if you want to help with tasks that need these particular powers. Wikipedia has plenty of very valuable and respected contributors who are not and do not intend to be administrators. Becoming an administrator also exposes you to a certain level of visibility and controversy that might not be desirable; often administrative tasks involve doing things that other people won't want you to do, such as deleting an article that they wrote. In general, becoming a possible administrator candidate is something that you should expect only after extensive work on the wiki, and not something you should strive for in particular. Admins have no fixed term of service, and particular duties are not assigned. Rarely, admins can lose their administrator status, though generally only if serious concerns have been raised and the Arbitration Committee has ruled on it.
Anyone can legitimately request help from an admin, whether on policy, technical matters, or when troubled by another editor. You can find a full list of administrators at [[Wikipedia:List of administrators]] (shortcut WP:LA). Checking this out is actually a farsighted thing to do. Early in working on the site, note those administrators who are active in your areas of interest. If a difficult issue comes up in a hurry, you can check whether a particular user is currently online by reading their contribution history (bearing in mind possible time-coding differences) and then leave a message on his or her user talk page. Or you can send an email to an admin who has enabled mail from his or her user page. Finally, you can go to [[Wikipedia:Requests for administrator attention]], which has a long list of the various places to ask for help with various problems, or to the [[Wikipedia:Administrators' noticeboard]], which is a discussion page just for requests and notices to administrators. This has the advantage that whichever administrators are active at that particular time will see your request.
You are obviously going to be polite in asking for help, so the next key point is simple enough: Be coherent and give the context. When asking for intervention, you must describe the contentious issue clearly enough so that someone else can grasp the problem at hand.
Requests for Adminship (shortcut WP:RFA) is the formal process of requesting adminship privileges, and it goes on in an open forum. Anyone with an account may request adminship; simply go to the RfA page and nominate yourself or (better) have someone else nominate you. Other people will comment on your application and ask you questions for a period of a week. Many criteria are discussed, mainly relating to the applicant's knowledge of administrator policy, but none have any official status. You obviously need to be a user of the site in good standing, but that rules out few serious candidates. Probably the best way to get a sense of the process is to review some recent debates; you can find archives at [[Wikipedia:Successful adminship candidacies]]. Once you have an account, you can leave comments on other applicants yourself.
After your nomination closes, a bureaucrat will evaluate the comments and decide whether to promote you; a 75 percent margin of support is generally required. Before trying to become an administrator, you should have at least a few months of experience editing the site and perhaps a few thousand edits across various namespaces. Experience in the areas that administrators work in, such as deleting vandalism, participating in Articles for Deletion, or particularly with helping smooth over controversial articles, is also recommended. Others will be assessing your grasp of major policies but also your coolness under trying conditions. Having a thick skin is useful and a level head even more so.
RfA became formalized as a separate area of Wikipedia in June 2003; until then, adminship requests were made on the mailing list. Before becoming an administrator was formalized even to that degree, administrator privileges were handed out fairly freely by Jimmy Wales to anyone who was a "regular" and known on the site.