A year ago, this website didn't exist. Now, it's at the top of this list of Internet resources for programmers! Stack Overflow is a place where programmers like you and me ask questions and answer them. Some things that make it great are: each question and answer can be 'voted' on (either +1 or -1), and the answers with the greatest number of votes appear at the top near the question; only programming related questions are allowed, and everything else is 'closed' down; any discussions on the answers go into the 'comments' section which is hidden by default - this means that flamewars and such nonsense are much less here, and mostly hidden from our view too.
But I can go all day about what makes it tick, but you won't really see how good a resource it is until you actually go there and try to search for some programming question you've been having. Chances are, someone else had it before you, and asked it there; in that case, you'd probably find very good answers to your question. If you are so unique that no other questioner thought of what you thought, you can login and post the question yourself - in which case you'd probably start getting answers within minutes, and the answer you wanted would be there within hours.
All that talk from me isn't probably going to convince you, so just go try it.
2. http://reader.google.com (actually, RSS feeds from programming blogs)
To be honest, this isn't a resource in itself, but can act as an aggregator of resources. If you're not familiar with the concept of 'feeds' or 'subscription' or 'RSS', here's a simplified view of it: when you add feeds from websites to Google Reader, you're asking it to check the sites for new content now and then, fetch the content automatically whenever it arrives and keep it stored, so that you can read it all in Reader without having to check each site yourself. If this does not seem like a big advantage to you (it didn't to me at first), start using it, and you'll see how much of a convenience it is.
The most important and common use of Google Reader (for us) is to subscribe to and read programming blogs such as Lambda the Ultimate, Joel on Software, etc., (in addition to webcomics such as Dilbert or xkcd :) ). Whenever you come across a blog that you consider interesting, click on the orange icon with the three curved lines that appears near the address bar (you are using Firefox, right?), and choose to subscribe using Google.
And after all this, don't forget to check out Google Reader every day or at least once a week. :)
While Google Reader might be the simplest for newbies (opinions differ even in this), there are many other feed readers and each one has its own fan base. ProBlogger seems to recommend FeedDemon, while other readers like the Sage extension for Firefox, Bloglines, etc. are also very popular.
Internet Relay Chat, simply put, is a set of 'channels' (what you might call chat rooms) each one devoted to a particular subject of interest. For example, there is a channel devoted to Wikipedia (#wikipedia I think), while another one devoted to discussions of mathematics (#math). You probably might find more use for ##c (for C programming), ##c++ (obviously, for C++ programming), etc. Like Google groups, here too, world experts on the field gather, so it's a very good resource if you know how to use it properly. If you're a beginner to IRC, I'd recommend the free IceChat client which is very newbie friendly and also powerful. The channels are hosted in things called 'IRC servers'. For programmers, almost the only server we'd need is irc.freenode.net. Connect to it, be polite, and share your knowledge too.
Known as 'Hacker News', it's a site where people post links to things they find interesting, and others vote upon them. This site is for 'hackers', and so though most of the content is about programming, other brain stimulating things that would interest a hacker would also be present. The ambience here is one of extreme decency and politeness, in contrast to most of the Internet. Some like the UI of the site, some don't, see if it fits you.
This site would have been much higher in the list if I had written this post a few weeks ago. But in that space, I've come to see that the discussions on Reddit (site #4 in this list) are usually much richer and informative than the ones here. Reddit does have other noise (people attempting at humour and nasty flamewars), but in trying to suppress that noise, HN (Hacker News) has seems to have suppressed some of the useful discussion too.
Even if you knew about all the other resources here, I'd bet you didn't know this one till now. From Regular Expressions to Functional Programming, there's a wealth of information about many programming topics. This along with Wikipedia can take your programming knowledge to a higher plane.
7. comp. heirarchy in Google groups
This is a whole list of 'Usenet' groups about computers. Within these, you'll most probably find the groups under comp.lang part most useful, but the others cater to special needs - for eg., if you're into programming for graphics, you might find the comp.graphics groups useful. These groups have lots of experts in the field of the group, which means you'll be interacting with top notch programmers in your area of interest.
A website where you get to 'compete' with other programmers from throughout the world in various 'tournaments', 'marathons', etc. Frankly though, I don't care a bit for the competition or ranking part of it. It contains so many good programming problems that, when you solve them, give you insights into so many things. Also, the Algorithm Tutorials here are said to be very good (they are on my 'to read' list :) ).
Some practical tips (since the UI of TopCoder is less than ideal and you might find it difficult to do things): To register, click on Login in the top right corner (you might have to scroll right a little to see it), then click on Register in the page that comes up. To participate in some tournament or just practice using questions from old tournaments, login to TC (that's the short form of TopCoder), click on Algorithm in the left panel, then on 'Launch Arena'. It would probably ask to install Java Web Start, go ahead and install it. After that, when the arena appears, login again in that window. Then, if you wanna participate in some tournament going on now (they'll send you mail about the schedules from time to time), choose the Active Contests menu. If you just want to try out old questions, choose the Practice Rooms menu. Either way, choose one of the SRMs from the menu. When you've been 'moved' to that room, click on the box that says 'Select one' and choose one of the scores listed there (like 250, 500 and 1000). A programming problem of that score would be presented to you. After this, I guess you'd be able to take off on your own.
There are other sites like Project Euler and Sphere Online Judge (SPOJ) which are somewhat similar to TC. Project Euler is heavily inclined towards mathematics, so I find its scope to be quite narrow. SPOJ is similar to TopCoder in that it too provides several algorithmic problems and allows us to submit solutions to be evaluated and validated. A small disadvantage is that the collection of problems is less than that in TC. But a great advantage in SPOJ is that it allows a wide variety of programming languages - TopCoder is limited to a few mainstream languages: Java, C++, C#, and VB .Net.
Thought the Internet is serious business, at times we need to take some time off to laugh out and relax. What if you can learn something while you do that? Well, the Daily WTF (they claim that it means Worse Than Failure) is a place for that. Working programmers tell tales about horrid code and other maladies from their co-workers, which are mostly because of a lack of programming knowledge. The stories are hilarious, but at the end of most of them, you'd be a bit wiser knowing a little more as to how to be a good programmer. Of special mention are the 'Featured Articles' and 'Tales from the Interview' sections.
Ok, I can hear your 'Duh!' even from here, but give me a few seconds. To be honest, no list ever can contain all of the wonderful programming resources out there. There are just too many forums, too many personal web pages that contain precious wealth of information. With some power googling (I'm planning on making a post on this soon), you can dig all that out. So, this makes Google probably the most useful resource for programmers. The only reason this is on number 10 is that you very probably know about it already (if you didn't, what forest were you living in? :) )
So, if I were to limit myself to 10, those would be it...
I know, I know, I probably missed your favourite website out of this list!
If so, do leave a comment here so that others (including me) might know and experience its glory. Thanks... :)