Well, define what a multitasking is.
There are several levels of multitasking.
level 0
you can have only one program open at the time. Like in good old DOS. If you want to copy a file, you have to close that word processsor you are using, go to DOS commandline, start Norton Commander, copy file, close Norton commander and go to DOS commandline, start word processor again, load document, find the place where you left off, resume work. Please note, that even with that super low level you had TSR programs
http://en.wikipedia.org/wiki/TSR_program , so you could use a mouse driver, or ansi.sys program to redefine keyboard shortcuts.
Level 1
best represented by a little known program called Dos Shell
http://en.wikipedia.org/wiki/Dos_shell . This *did* have a kind of fake multitasking. You could run a text editor and if you needed to copy a file for a friend you pressed a secret key and the system would start a TSR that swapped your opened text editor away (it could not swap it to disk, that came with the first windows) let you copy the file and then you could return to your text editor and continue.
I call this fake multitasking, because at the time you were away from your text editor the application was completely inactive. So if you started, for example a "find and replace" process, and went away, it would not run in the background.
Another example is The famous Dos Navigator that let you run several of its components at once, even playing music in background or performing an operation when you were away.
Level 2
- the kind of multitasking offered by Windows 3.0
Level 3
- the multitasking in Windows 95, where you could perform several operations at the same time, as long as you were not formatting the floppy disk at the same time ;-), or copying file through parallel port using laplink cable, or using modem, or ...
level 4
- what we see in Windows XP. Many people would argue that even this is not the TRUE multitasking. Just ask any Linux, Solaris or even MacOSX

fan. If one program seizes it can bring down the entire system.
See
http://en.wikipedia.org/wiki/Computer_multitasking
To sum it up.
As long as each application remembers the state where you left of (switched to another application) and some applications would let you to, say, play an mp3 file in background you do not really need true multitasking MOST OF THE TIME. This is how most PDA-s operate.
You are not going to run an app to rip a DVD in the background, you are not going to watch video while working on a spreadsheet.