There's a few preliminaries before I actually get to whether it's "worth" it (in this cause, worth being what you get out of it). Firstly, Linux is a kernel, around which distributions are built. Distributions are comprised mostly of GNU and GNU-licensed software, as well as other "free" software (usually both in the sense of free beer and freedom, but in general "Free" means "Freedom" when it comes to free software. Another, more specific term, is FOSS, or Free and Open Source Software.) that maybe under a variety of licenses.
Anyway, you are correct that it is free (as in freedom and free of charge) and can be modified, albeit extensively. "At any time" is a bit nebulous, as it implies that there are haphazard modifications and such, which usually is not the case. The Linux kernel itself goes through versions and revisions, using code from all over the community in combination with Linus' code. A well maintained Linux-based system can be extremely reliable. A lot of servers use Linux distros as their operating system (not to be confused with their
web server, which is Apache.) Basically, as long as you're willing to read the docs (which are easily avaiable via
man <application> or through searching the Internet.
But... I would say the value of a Linux system is really in the user. Is he going to be programming a lot, running a home server? Does she like to tinker and play around with her OS? I would say that Linux/GNU/FOSS, etc. is just a different way of approaching computing. It isn't for everyone, but it really does resonate with some people. Linux and the software often used with it is very community based, meaning that it's not so much a closed hierachy, as with closed source, but a more meritocratic community, where it's based more on your ability and what you know. This shouldn't turn you off from using it though, there's many Linux distributions that are very easy to use, such as Fedora (I personally wouldn't recommend Ubuntu, although some would). And of course, if you take interest, there's really no limit on what you can do.
So, it dependings on *you*. What do you want out of your OS/computer? What do you want to do? In general, Linux tends to be more programmer/hacker (hacker as in
this definition) friendly, and geared towards more technical users. But many distros are easy to use. Basically, just pick one and try it out on an old computer or you can download a distro like Xubuntu and install it via WUBI, which will let you still use Windows as normal, but also have the distro (kinda like dual booting).
One thing to consider, is that Linux is definitely not for everyone, and not for people who don't like to experiment. It takes a lot more patience and time to set up than Windows - although that can be dependent on which distribution you choose - or Mac. It doesn't do much for you. If you don't want to take the time to setup a lot of stuff, the go with Fedora or Ubuntu, they do almost everything for you. Once installed, you just start browsing the Internet, or doing whatever. Word processors are usually included. But if you're like me, you can go with a simpler distribution like Arch or Slackware, but I would NOT recommend those if you've never tried Linux before, you'll get turned off immediately.