Can malware change words that I have typed and then saved in the computer'? If so, how likely is this?
If a malware infects your machine, it will have access to everything on your machine and potentially other vulnerable machines on your network. As a consequence, the malware will be able to modify any files on your machine, including but not limited to text files of any kind.
To fix this, there's only one thing that can be done to be sure - wipe your hard drive and reinstall your operating system. If you were infected with a known and cleanable malware, it's possible to get away with only wiping your system drive and then systematically cleaning the other partitions, but that should only be done by someone who knows what he's doing.
Depending on the type of virus, then it can do anything. If you have a virus that masquerades as a motherboard driver, then it can potentially overheat your computer and burn out the motherboard. If you have a virus that's running as a daemon under your local account, with UAC enabled on Windows, then the damage it can do is limited - it can spread over the network, it can infect other files that it has access to, and it can create, delete, or modify the contents of any file it has access to. If it's running with elevated access or under an administrator account with UAC disabled (or UAC enabled but you've given it permission to elevate its privileges by clicking the allow button), then it can potentially create a file anywhere on the system, delete a file anywhere on the system, and change the contents of a file anywhere on the system.
Most viruses aren't interested in changing files, but they are interested in deleting them, infecting others, spreading over the network, and being major annoyances. You should run antivirus software all the time, and you should only download files from sites you trust so that you can protect all your data and avoid having to format your hard drive.
Quick update: This article I just happened across talks about a good example of a virus that exists solely to ruin your documents.
Like others have said, once malware has successfully infected your system, it can do anything. So yes, it certainly can corrupt data in such a way.
More to the point, what you are asking about has actually been done in a sense, and quite long ago at that. I don't know if there's any current malware which behaves like you are asking about, and it might not have been the first to employ such a technique, but the original Dark Avenger virus overwrote random locations of the disk with a specific message back in 1989. Those overwrites could easily corrupt both file system metadata, documents and executable files, depending on what happened to be in those particular parts of the disk, and since the writes were random and progressive it could take a fair while before you'd notice that something was wrong.