Q:

In teaching, what are the advantages of using slides over doing board work?

At my university, most lecturers and professors use slides in teaching. This is true for most engineering, mathematics and science courses. I am more comfortable with doing the board work and then sharing my hand-written lecture notes with the students. From my personal experience, I feel that the latter is a better way of teaching.
So, what are the advantages of using slides? Why do you use slides?
Secondly, does the answer to the above question change if you were teaching graduate students?

A:

I am a student and I much prefer lecturers who write on the board than the ones who use slides.
Profs using slides generally go into loop mode where they have the objective of going through all the slides before the end of the class. As such, profs tend to go in a very fast pace.
Writing on the board brings some dynamism to the lectures. The lecturer tends to pace himself much better, and students are then more encouraged to ask questions as they go along. 
Also, having students write notes help them become more active and aware during the lecture.
In my experience I've seen lots of profs who just read the stuff from their slides without elaborating any further. The students then tend to fall asleep since they know the lectures are basically in the slides. 
Also, I have the impression that profs using slides are lazier in their teaching, in the sense that they don't even review the slides they are about to present before the lectures.

A:

Advantages of slides over boardwork? Laziness, clean hands, digitally distributable product that represents all the work you didn't actually demonstrate in class.
And... those are also the disadvantages.
Board work is usually more engaging, and at least the classes I've taken and given, board-based classes kept the students (and the instructor!) mentally and verbally engaged in the material. Its naturally more exciting to watch an animated instructor write things out, check himself mentally for a moment, subconsciously sharpshoot him yourself as he moves along, etc. than to just listen to what may as well have been a recorded session flashing by on screen.
People who write on boards tend to only write the important bits on the board, and have prose handouts full of other details for reading and reference later. The constraints of live board work perform a magically precise editorial function which forces the instructor to either be concise or fail. Handouts retain every benefit of the slides but without exposing the instructor to the temptation of drifting into a passive or mentally absent teaching mode.
This is particularly important in graduate or corporate classes where the material may be new, originated by the person teaching and not yet fully baked (a wonderful situation where the gallery's questions actively deepen the instructor/researcher's knowledge right then -- is there any greater ideal?). People who write on boards usually have either rehearsed their material or know it intimately enough to pace through an essentially hands-on class as they go -- even (or especially) in the case of new research. This is as good as it gets for live instruction!
And this leads me to the worst thing about slides...
The laziness permitted by slides is paradoxically compounded by the temptation to be verbose in the slides themselves. This is the worst form of detached instruction and often devolves to the point that the "instruction" consists of an underprepared instructor who feels prepared (he's got his slides, right!) essentially reading whatever is written on the slides to the class. In these cases equal time spent with a book in a quiet place benefits a student more than having suffered through the presentation. Such sessions are a sad satire on modern pedagogy; but satire is not what your students came for.
The points above also happen to be relevant in organizational briefings. The cardinal rule is that the person doing the talking is the class, not the board or slides or other AV assistance. Someone with something to say who knows how to say it doesn't require anything but his energy and voice -- the other stuff is either enhancement or distraction.

A:

Slides can be great to force you structure your lectures before class and actually stick to them, and they are always more legible than writing on a board (plus less messy if you have to deal with chalk rather than a whiteboard).
That being said, the slides remove some of the dynamism from the course in that they have students think less critically than when watching you work with a board. Part of this disengagement simply comes from lighting, but another part comes from the way that slides can't easily be amended during a lecture.
The most fun aspect that I've noticed when I use boards is that the students who are taking notes write down everything that I write on the board. Those notes are much less structured than what I could produce with slides that they would later download, but the actual process of writing out the notes keeps students mentally engaged as well as promoting a discussion rather than just a lecture.

