Every librarian will tell you that you should be careful when using the web as a research tool. Anyone can put anything on the Internet, and a quick Google search can very often take you to convincing-looking hoax websites like this one, as likely as it is to get you something good.
The online resources you can get through your school/public/University library will give you access to trusted, suitably regulated and peer reviewed information of course, and that's one reason why we still need libraries.
But some librarians, gatekeepers of knowledge that they are, have also generously put together some websites that collate the best of the web that each and every one of us can access from our own computer at any given time. Here are a few that I use:
Run by a thousands strong conglomeration of information professionals, the Internet Public Library handily breaks its websites in to easy to navigate subject areas. The special collections usefully focus on topical issues (albeit with a slight American bias in some cases), and there are kids and teens sections too! To top it all of, you can ask an ipl librarian for help if the website can't locate what you're after. Highly recommended.
For the serious researchers among you, the closest thing the web has to a UK University library style website. For popular culture, look elsewhere, but for academic, scholarly disciplines there is no better place. Due to funding issues, Intute stopped adding new resources last year, but it is maintained, and the Virtual Training Suite is excellent.
The best of the web laid out in the form of a library: i.e. in Dewey number order. See it as good practice for browsing the non-fiction shelves at your local library! The biggest plus of this is that it keeps things in neat, categorised, library-like order. The breadcrumb structure is logical, and more popular categories (in bold) usefully break down lists of further websites.
Run single-handed by the quite heroic Margaret Vail Anderson, Digital Librarian's homepage alphabetises the world's knowledge as opposed to Dewey decimal them. Things are kept alphabetical once you click on the relevant subject link, and those who hate large amounts of text may struggle with the comprehensive lists. But the 'See Also' breadcrumbs are useful.
The time you'll save looking at these instead of pulling up millions of hits on a Google search is unbelievable. I'm not saying never use Google or Wikipedia again (they're both perfect for quickly finding out something). But as tools to help you find reliable websites you need for proper reseatch purposes in a reasonably painless manner, these can't be beat.