As a teacher in lower grades of high school (mostly 10th graders), I find Twitter to be more of an annoyance than anything else.
Wikipedia, however, has a lot of benefits when used correctly. When I have students do research, I send them to Wikipedia first to get a general feel for the topic. Say they're researching Miranda V. Arizona (I teach a projects-based law class,) Wikipedia will give a general, concise explanation of what that case is about, its issues and some of the areas surrounding the case. It also serves as a springboard to more scholarly sites and sources. If you look at law sources on the web, they can be pretty daunting for the average 10th grader, as many of them are designed for use by lawyers, law students or poli sci students. More so if the student has little to no background knowledge on the topic to begin with. Wikipedia provides enough background knowledge to fit in more important, scholarly details, and that aspect of learning is often overlooked by the /. crowd from what I've seen.
Do keep in mind that while you are probably brilliant, you had to start somewhere. For many things, and for your average student, Wikipedia is a great portal to start with, although as stated by an earlier poster it should NOT be the only source. There is a reason that the people blasting Wikipedia tend to teach at the college level and AP or IB level classes. Mainly, the students in those classes should already have the ability and desire to access that generalized information.