The problem with fixing something that frustrates YOU is that you're facing a LOT of competition. That strategy might work for 37signals but it won't work for everyone (just take a look at the gazillion of web apps aimed at developers/designers/entrepreneurs/etc.). I would say your best shot at finding a profitable idea is to explore an industry/domain that is under served by developers.
Read books, trade magazines, blogs, etc. in an industry that is unrelated to software development/social media/freelancing/etc. You will find that some of these industries are under served and are oftenly not up-to-date with the latest technologies.
I totally agree with the whole "fix a problem" mantra, but try to find problems that not too many web entrepreneurs have. Think outside of the box !
Find a pain point and fix it. Every time something frustrates you, try to solve it for you and everybody.
Is there anything you're missing in your day to day?
When you're getting your job done, or you're working on your personal stuff, do you sometimes think "if there only was an app that I could use for this..."
List all of them and then try to figure out which one could have the best traction to a wider audience.
You need to remember that a good web app needs to provide instant gratification to the users (you sign-up to use it, and get immediately hooked to how it works and what you can do with it). Be sure you use this criteria when going through the list of ideas you gathered.
I don't think my previous post made it through.
This site is a great source of ideas (and not just under the 'ideas' tag). Look at this post - Framework for Freemium Model in ASP.NET - does that not indicate to you that there may be a market for an easily usable Freemium plugin for various web frameworks (not just ASP.NET but RoR and Java).
Here is someone who has a great OCR algorithm - any immediate thoughts on how it could be used? I would like an app for my Android phone (I guess iPhone and iPad users would like it as well) that I can point at random text (poster, flyer, etc) and send HTML or PDF directly to my blog or via email.
The platform this site is running on may be shutting down. Come up with something that has the same facilities but a better revenue stream.
There are often people looking for funding for their start-ups. Is there a way you could facilitate that? Niche sites may get a lot of funding from their users (who don't want them to go away and don't want to have to migrate their data) in return for discounts or equity. This one is a bit complex (legally & financially) but certainly puts the Internet back in the hands of the users rather than the corporations.
There are four ideas just from looking at the front page of this site at close to midnight (my time). The problem is not ideas but how to implement them (you got that in the first reply though).
I agree with the whole "fix a problem" theme from the other comments. Some thoughts on how to find the right one: