Update 1/5/2018 - over the last 9 years, my thinking has evolved considerably on this topic. I tend to live a little closer to the bleeding edge in our industry than the majority (though certainly not pushing the boundaries nearly as much as a lot of really smart people out there). I've been an architect at varying levels from application, to solution, to enterprise, at multiple companies large and small. I've come to the conclusion that the future in our technology industry is one mostly without architects. If this sounds crazy to you, wait a few years and your company will probably catch up, or your competitors who figure it out will catch up with (and pass) you. The fundamental problem is that "architecture" is nothing more or less than the sum of all the decisions that have been made about your application/solution/portfolio. So the title "architect" really means "decider". That says a lot, also by what it doesn't say. It doesn't say "builder". Creating a career path / hierarchy that implicitly tells people "building" is lower than "deciding", and "deciders" are not directly responsible (by the difference in title) for "building". People who are still hanging on to their architect title will chafe at this and protest "but I am hands-on!" Great, if you're just a builder then give up your meaningless title and stop setting yourself apart from the other builders. Companies that emphasize "all builders are deciders, and all deciders are builders" will move faster than their competitors. We use the title "engineer" for everyone, and "engineer" means deciding and building.
Original answer:
For people who have never worked in a very large organization (or have, but it was a dysfunctional one), "architect" may have left a bad taste in their mouth. However, it is not only a legitimate role, but a highly strategic one for smart companies.
When an application becomes so vast and complex that dealing with the overall technical vision and planning, and translating business needs into technical strategy becomes a full-time job, that is an application architect. Application architects also often mentor and/or lead developers, and know the code of their responsible application(s) well.
When an organization has so many applications and infrastructure inter-dependencies that it is a full-time job to ensure their alignment and strategy without being involved in the code of any of them, that is a solution architect. Solution architect can sometimes be similar to an application architect, but over a suite of especially large applications that comprise a logical solution for a business.
When an organization becomes so large that it becomes a full-time job to coordinate the high-level planning for the solution architects, and frame the terms of the business technology strategy, that role is an enterprise architect. Enterprise architects typically work at an executive level, advising the CxO office and its support functions as well as the business as a whole.
There are also infrastructure architects, information architects, and a few others, but in terms of total numbers these comprise a smaller percentage than the "big three".
Note: numerous other answers have said there is "no standard" for these titles. That is not true. Go to any Fortune 1000 company's IT department and you will find these titles used consistently.
The two most common misconceptions about "architect" are:
These misconceptions come from a lot of architects doing a pretty bad job, and organizations doing a terrible job at understanding what an architect is for. It is common to promote the top programmer into an architect role, but that is not right. They have some overlapping but not identical skillsets. The best programmer may often be, but is not always, an ideal architect. A good architect has a good understanding of many technical aspects of the IT industry; a better understanding of business needs and strategies than a developer needs to have; excellent communication skills and often some project management and business analysis skills. It is essential for architects to keep their hands dirty with code and to stay sharp technically. Good ones do.