I didn't have any formal training in public speaking until it was time to start presenting departmental seminars as a grad student, but I had a lot of informal training as an undergrad. I got involved in a number of campus activities, such as our orientation committee, where we'd prepare workshops for freshman on various things that would help them with college life or other aspects of life (these varied from things like basic car maintenance for the commuters to time management or organizational skills). While running those workshops, I got a lot of practice with public speaking, though they probably would have gone better had I had more experience at the time.
In grad school, the biology teaching assistants were given quite a lot of training about how to teach, which of course includes speaking to groups. We also had department seminars and all grad students were required to present their research once a year (not just after you passed qualifiers like many places, but from year one...in your first year, it was expected you'd present a proposal of your research ideas if you didn't have data yet). Most of our grad level courses required some form of presentation as well, either presenting a paper as a journal club format or presenting a proposal based on a topic we'd been studying. In one class, we had to write exam questions for each other and were graded both on the questions we asked and how we answered those asked of us...talk about a true challenge, there was no way to predict based on what a professor emphasized just what question you would get, and we each had two questions to answer orally for our final exam. We were all nervous about the idea, but it turned out pretty fun.
I also taught a workshop on public speaking and communication skills to the students in the dorm I worked in when I was a grad student (they were all math and science majors and of all the workshops offered, mine was one of the more popular ones).
I'm quite glad of all the public speaking experience I have. Last year I gave a talk at a conference and had numerous people come up to me after the talk was over just to comment on how much they enjoyed my talk. I know it's always what clinched the deal of me getting the post-doc position I had (I was told later that the program director had commented after my talk that he wished more people gave such good talks).
More than just content, style counts for a LOT in public speaking. Body language, using a pointer in a way that's helpful and not distracting, facing your audience, speaking loudly and clearly and enunciating every word, using visual aids that are meaningful to the audience, being sure there's a theme to your talk and that it's organized, looking relaxed but not too casual, being conversational rather than "preachy," etc.
In our own program, I see a lot of variation among the students giving seminars because much of the public speaking aspect of their training is left up to their individual mentors. There are a number of students who really could benefit from a more formalized approach.