Given all the rules governing propriety for elementary school students these days, it would seem that the selection of topics for persuasive speeches would be somewhat limited. However, some interesting unusual topics would not offend the sensibilities of school administrators and teachers. Animals, particularly strange ones, always make for good speeches. "Why Wombats Make Good Pets" would make for a particularly interesting topic, since most students will have never seen a wombat, much less know why they would make a good pet. For older kids, zombies seem to be in vogue as of 2011; a speech on "Why You Should Believe in Zombies" should generate substantial interest.
The challenge for high school students centers on finding a topic that is current and edgy yet does not run afoul of the limitations put in place by school administrators. At this age, students are just beginning to become politically aware, but arguments over the best political party have just become so routine --- unless you take a risk and try to persuade people "Why Anarchy Rocks," fpr example. Such a speech would serve to be both instructional, defining anarchist political philosophy to students who likely know little about it, and entertaining. At the opposite end of the spectrum, in the realm of the nonsensical, the topic "I Like Pie" could be a dissertation on the advantages of pie over cake --- a relatively insignificant, but age-old, debate.
College communications classes are generally anything goes, and it may pay to be somewhat shocking, provided you don't go too overboard. Titillating topics such as "Why Football Is Better Than Sex," or those that are just so off-the-wall as to be just silly, such as "Why You Should Ride a Polar Bear to School," will have your audience dying to hear how you came to just such a conclusion. As with high school speeches, you could examine alternative political theories yet with much looser restrictions on content, the greatness of such political platforms as those of the Pansexual Peace Party or the Scorched Earth Party (these are actual political parties).
Business professionals must remain aware of their audience. Choosing an inappropriate topic, even in an ostensibly non-business setting, can have a long-term detrimental impact on business relationships. As a rule, avoid the two major topics that cause the greatest controversy: politics and religion. Strange, offbeat and amusing topics that are non-offensive can include "The Twinkie Standard --- The Argument for Snack-Food-Based Currency" or "The Yugo --- Why the Disposable Car Was an Idea Ahead of Its Time."