TrueCrypt works by creating virtual encrypted disks; this means that, as far as Dropbox can tell, a TrueCrypt-encrypted disk is just a blob of random binary data. However, when you mount that volume using TrueCrypt, you need only enter the correct password and a new drive shows up on your system. Every file you put into this drive is instantly encrypted, secure from prying eyes. As soon as you unmount the volume (eject the disk, so to speak), it becomes completely inaccessible.
TrueCrypt is very serious about security, to the point of providing plausibly deniable encryption. Let's say that some person or legal entity finds out you're keeping files inside a TrueCrypt volume, and has the power to compel you to give away your password. With a less serious security solution, this is game over: As soon as you give over your password, your data is forfeit.
TrueCrypt lets you get around this limitation by creating a hidden volume inside a TrueCrypt container. Enter one password to decrypt the volume, and you get one set of files (decoy files you put there in advance, which should seem believable enough to stand in for the contents of that volume). Enter a different password to decrypt that same volume, and suddenly you get an entirely different set of files, which are the real files you're trying to protect. In other words, whoever coerced you to give away your password now thinks they have whatever files you were hiding, when in fact they don't (but you can claim they do, and there's no way to detect that two-password trick). This sounds like a scenario lifted out of a William Gibson novel, but it's a great option to have, especially in a free tool.
For browsing securely: Tor Browser Bundle
Judicious use of KeePass and TrueCrypt is more than enough for creating a very secure environment. We now officially leave essential apps territory and enter realms of luxury (or paranoia, depending on how you look at it). If you want to beef up your Internet browsing security as well, the Tor Browser Bundle is the way to go.
The Tor network provides a way to browse anonymously. When you connect to Tor, all of your Internet traffic is encrypted and routed through a complex network of anonymous nodes until it reaches its final destination. It's not 100% secure, but then again, no security solution is. Tor has been around since 2002, and has been field-tested in rough situations in Egypt and other oppressive regimes that restrict Internet access. It works.