While most consulting falls under the rubric of management consulting, there are a diverse set of other areas where consulting is provided. Broadly speaking, the job requirements are as follows:

People skills: High
Sales skills: Medium
Communication skills: High
Analytical skills: Extremely High
Ability to synthesize: High
Creative ability: High
Initiative: Medium
Computer skills: Medium
Work hours: 50-90/week

Some general observations:

Consulting is an exciting but risky profession
The work is stimulating and important, but not everyone lasts in this business.
Consulting is About Business.
Consulting is the business of providing advice to firms in trouble; firms on the move and firms which are trying to do what they do better, faster, and more cheaply. Consulting is about business. People who love business like consulting.
Consultants Listen
Consulting requires the ability to listen to your customer; it also requires the ability to explain to your customer. Consulting is about communication. Good communicators do well in consulting.
Consulting is a Profession that is Growing
The business of consulting has been growing by leaps and bounds in the last decade. There is a lot of hiring going on and there is likely to be strong demand in the future.
Not Everyone Starts on Top
You would usually start in an analyst position. To succeed in these positions you need to be extremely dedicated and be willing to travel. Many, but not all, positions are grueling because they require long hours and heavy travel.
Network, Network…
It’s important to have a good network of business contacts in consulting as you progress. New business development becomes part of your job. As your classmates rise in their respective business areas it is important to stay in touch with them as they may become your future customers.
Teamwork, Teamwork…
A key to success in consulting is teamwork. Being able to pull together persons with large egos to get a presentation together for a client is a challenge and is likely to be rewarded highly. You will almost always work as part of a team.
Brainwork, Brainwork…
At it’s essence, consulting is using stretching and using your brain.
A consultant sells ideas, smarts, brilliance (and, of course, talks a lot about transforming ideas into action). People with serious smarts and analytical firepower are in constant demand from the very best consulting firms.
A Different Perspective Can Work
Candidates with original perspective wanted.

Consultants listen, analyze and solve. To put it all together you have to be able to look at things differently than the average manager out there. If you’ve lived in a different country, or have a strong background in a non-business area like literature, music or biology, you may have just the type of thought-process a consulting firm is looking for.

Industry Knowledge Counts.
If you have serious experience working in a specific industry, be it utilities, paper, airlines, retail or financial services, there probably is a consulting firm looking for you. Firms want specialists with deep knowledge in specific industries who can understand the present and envision the future.
Presentation skills matter.
If you can understand a clients needs, help them formulate a solution and then present your findings effectively, whether it be one-on-one or in front of a crowd with the latest multimedia technology, you will be in demand. Ability to present well is something that takes hard work for almost everyone. Try to convey your commitment and ability in this area.
Powerpoint Skills Are Important
Similarly, the ability to make a good presentation is very important and some firms like Bain and McKinsey have taken Powerpoint presentations to a high art. Gary Zelazny, McKinsey’s Director of Visual Communications, has written two books on good presentations and charts which are of nearly biblical importance for serious consultants.
It’s Not Always Fun…
There are plenty of time when the work is less than glamormous.

Taking an idea you already understand and applying it to a new client. Or doing laborious industry research. Or using simple common sense on clients that don’t need a Ph.D., just a kick in the pants. Be sure that you have realistic expectations about what the work is like day to day.