Could multiple advisers mean that it might be easier for you to get funding? (since you're not just limited to one person?) Could it also mean that you get more overall input in your project (the input of 3 different people), and that maybe your project will be geared in a way that it's "interesting" to more people, and consequently might also get more citations that way?
They might pull your project in different directions, but how much is this really a concern?
And what about the special case where they explicitly expressed the desire to interact with each other more through the student? (this was actually the case in my situation).
The answer (as in case of most answers in academia.SE) is it depends, often widely from case-to-case. Unless presented with an exceptional example, I would generally view having more than two advisers as a major hindrance - the perceived benefit of having another source of ideas is negated heavily by the communications overhead between them, and the scope for misunderstandings about their role, which might cause the student to be either overloaded in multiple (possibly conflicting) areas, or languishing without any significant guidance. The rest of my answer is based on the assumption that the number of advisers is 2.
What is the defined role of the said advisers - are they equally responsible for guiding the student towards completion of their graduate studies (as I've been told is the case in some European schools/research schools), or is one of them the principal guide and the other a co-guide? The amount of time/effort invested by each would depend on their perception of how much they are actually responsible for the student's growth as a researcher.
As with most social interactions, it would help greatly if there is a good (or at least professional) working relationship between the 2 guides, as well as a healthy overlap of research areas - a new student might not be able to handle multiple research problems in completely different areas at the same time (without affecting the time to graduate, or the quality of results).
Assuming the student publishes with both of them independently, it would look good on her CV that she can produce publishable research with multiple established researchers. This could also have the side-effect of enhancing the student's research network - as a lot of papers (in CS at least) have more than 2 authors, and often collaborating on an paper could lead to more papers/research done with the same set of persons in future.
I think it's detrimental to research progress to have more than two advisors "in practice." (By this, I mean that there should not be more than two people directly involved in day-to-day matters. A "formal advisor" who does not play a substantial role in the thesis would not count.)
There are a number of reasons for this:
It can be very difficult to get all of the advisors together in the physical sense, and even harder to get them to agree on anything, when they all will want to have their viewpoint considered and accepted.
A substantial part of your time as a research student may be spent "translating" back and forth between the different advisors. On the other hand, this can also be a potential strength, in that you will have to learn how to make arguments using several different research "languages."
Funding and bureaucracy will become more complicated the more advisors you have. (This will be true for multiple advisors, even if some of them are "hands off" or formal rather than practicing advisors.)
So, in general, it's best to have one or two advisors.