First, a little background. I switched to slides a few years ago when teaching a 3rd year course at my university. Because of how teaching works at my university, this course is one of the first where as a lecturer I can assume that the students taking it are interested in mathematics as a subject in its own right. That is, they aren't students from another program taking it because it is required of them. This doesn't mean that they are all mathematically sophisticated -- in fact, they tend not to be -- but rather that they are expected to learn about how to do mathematics from the inside. So there are proofs, and proof techniques, and the like. It's also a fairly diverse course with topics from metric spaces to linear algebra to Hilbert spaces. (Finding a common theme through that lot was one of my difficulties in the early days!) Lastly, for background, I teach in English but the majority of my students have Norwegian as their primary language.
I taught the course using chalk the first time that I taught it, and then switched to slides the second time. I then taught it three times using slides before it passed on to another lecturer. The last time that I taught it, I was awarded the faculty prize for "Teacher of the Year", primarily for that course. I won't say that it was the slides that won it, I mention that to show that it was part of a general strategy that worked. On that, I can also mention that enrolment in this course also increased over the four years that I taught it, to almost double its initial numbers. Also worth knowing are that I experimented with slides before this course with a half-and-half method (on a different course) and it was the feedback from that which convinced me to try the full method, and that after teaching that course then I also taught a lower level course with slides and for that course then I have moved back to using chalk.
Here's what I was thinking when I switched, plus some commentary on whether it worked as I expected.
My primary consideration in switching was to consider the question "Where is a student's attention during the lecture?"
I completely agree with the theory that students learn by doing, and I love the idea of an inquiry-based course and of interactive lectures with communication in both directions. However, I'm not convinced that the lecture has to be where the students learn. In a course like this one, I saw the lecture primarily as the demonstration where the students would see what they should do and then they would go to their own labs and try it out. So the lecture is primarily to communicate mathematical thinking. Yes, a lot of knowledge as well, but never bare facts (definitions or theorems or even proofs) - every definition comes with a story as to why it is that definition and not another, every proof is ladled with detail as to why each step is the natural one.
In this, then, the desired focus of the students is on me. I am trying to demonstrate what is going through a mathematician's head when (s)he contemplates a mathematical problem.
So what happens with a chalk talk? I say something, the students obediently listen, then I write something which the students obediently copy down. I then wait for them to finish writing, which some do quickly and some do slowly, before saying the next thing which half of them miss because they're still copying down the last thing I wrote. In addition, some of them are having difficulty copying stuff down because I wrote it in English and their mental error-checking codes are set up for Norwegian.
Using slides gives me the following advantages:
No time is wasted through writing. What I write appears on the screen so I don't waste time. I always make my slides available in advance (as both "presentation" and "handout" versions) so the students do not need to copy things down during the lecture: they can print them out and bring them along and make additional notes if they want but don't have to.
I know exactly what the students are looking at. Yes, when new stuff appears on the slide then the students look at the slide and read it, but I control when that appears and I know what it will be.
The students know what we will cover. They can see the slides beforehand and read them (if they want). I also provide references to the text book(s) or other resource pages for background material.
The students know that they will have the notes that I meant them to have. So they don't need to worry about missing a word in a definition or misreading a symbol.
I'm not quite sure where to put this next point so I'll put it here for lack of anywhere else. I only switched to slides when I knew that the technology could support it. I did not want to remove the flexibility of chalk so I needed to know that I could go "off piste" if necessary. To that end, I started out using a graphics tablet with (a slightly hacked version of) xournal. Once I had an iPad, I switched to that. My handwriting leaves a little to be desired, but nevertheless is workable. In addition, I supported the in-lecture material with a wiki and a forum to provide out-of-lecture support. This is how I got around the perceived inflexibility of slide lectures. The annotated slides were published after the lecture, so if I wrote something on the slide then the students didn't have to copy it down as they knew they'd get access to it later that day (this is one reason why I heartily dislike using slides and chalk, the other reason is to do with the lighting in the lecture hall).
Once I'd embarked on using slides, I encountered other advantages:
It forced me to prepare in advance and prepare well. Since my plan was to get the lecture notes up in time for the students to print off before the lecture, I had to have the lecture prepared the day before, not the hour before. In addition, as the notes were what the students would see and not just hints for what I wanted to write, I had to check them carefully. So I couldn't assume "Oh, I know how to do this" and not bother to prepare each example carefully.
It forced me to keep to time. I integrated my slide preparation with my lesson plan so I had planned how long to spend on each topic. If I changed the timings in my lecture then I had to have a very good reason for doing so. Note that I could change my timings, but wouldn't do so on a whim.
It forced me to think very carefully about what the students could see. It quickly became clear that the best slide was a blank slide, and that it stops being optimal when you start adding content. So the trick is to figure out just what you want the students to be able to see at any given point and put just that on the slide.
It forced me to think from the students' perspective. Since slides put me in full control of the lecture hall, I had to think a lot more about how the students would react and what they would need to know and when.
It gave me more flexibility in how to present material. Of course, once can always go too far (and some may argue that I did), but I think that it is much easier to be creative with slides than with chalk. An example that springs to mind is stepping through the proof of why the space of continuous functions is complete. I would have the same "slide" with small changes each time and a commentary on what was happening in each step.
In addition, once the computer (or iPad) is in the room and switched on, it becomes easy to use further functionality, such as animations or videos. It's all very well to talk about the SVD of a matrix, but there's a nice animation of why it works for 2x2 which makes it much clearer.
The main disadvantage that I encountered with using slides was the time taken to prepare the material. And even though I could re-use them the next time, I still wanted to tweak them and so it didn't cut down as much as I'd hoped.
All that said, as I mentioned above then I've stopped using them in the lower level course that I currently teach. I'd say that my main reason for doing so was that I felt that the students didn't know how to cope with maths being taught via slides. I don't think that they knew what to do with themselves in the lecture hall: they came to get a set of lecture notes and since that was being provided for them without them needing to do anything else, they didn't do anything else. So ultimately, whether they work or don't will depend on the students. The goal is to get the students learning and if they can't or won't learn from slides, there's no point in using them.
You can find slides from my lectures from links on my teaching page. The course that I'm talking about above is TMA4145; TMA4190 was my half-and-half experiment; TMA4115 is the lower level course. Some of the notes are located on the mathsnotes wiki, linked from the above teaching page.
 I don't mean anecdote here. I mean more in the flavour of an explanation.