The Mac Plus, a compact Mac with one internal 800 K floppy, but without an internal hard disk and a fan (making it very silent), is the floppy driven Mac pur sang.
Because I'm allergic to noisy scsi peripherals like external hard disks. I boot my Mac Plus from a floppy disk.
How does this work? And can I run anything besides very old 50 Kb programs?
This depends on your wishes and your hardware. Questions arise like: do you have an external floppy drive next to the internal one in your plus? How much Ram do you have installed?
Here are some examples about dealing with floppy driven Macs.

Case study one:1 Mb Ram, 1 800 K floppy drive
We use a minimal system here. Forget about multitasking. One might even consider running some older (less disk space consuming OS) like system 2.01, in order to have enough disk space left on the floppy for on application and some documents.
What to put on the disk?

system 2.01 setup
one minimal system folder containing:
Clipboard file: 1 K
Finder 79 K
System 233K (can be made even smaller by removing unnecesary fonts and DA's.
Total: 313 K, ca. 487 K left. Wanna add a laserwriter driver: 75 K extra. (laserwriter drivers are the most economic because all inkjet printers need much larger drivers) ca. 412 K left.
When looking around for old software you might find a word processor that takes about 100 K. Meaning you'll have 312 to 387 K left for documents

Case study two: 1 MB, 2 800 K floppy drives
Now we have whopping 1600 K storage space instead of 800 K. That leaves plenty of space for more fancy stuff. you might consider intalling a more 'modern' system folder and a small but nice word processor on the system disk and using the other floppy drive for storing documents or, when you need to relax, play a game that fits on a 800 K disk.

System 6.05 setup:
one system folder containing:
AutoIdle 10 K (a small screensaver is very healthy for a Compact Mac)
Backgrounder 5 K (for background printing)
Clipboard File 1 K
Finder 108K
General 14 K (control panel)
LaserWriter prep 28 K
LaserWriter 64 K
Multifinder 50 K
Print Monitor 37 K
Startup finder 1 K
System 212 K (all unnecesary fonts and da's have been removed)
Total: 530 K. Leaving 270 K free for an application such as a word processor, some disk space for printer spool and maybe some extra control panels or AppleShare (45K). The other floppy drive can be used for floppy's for storing your docs, playing an occasional game or whatever you want.

Case study three: 4 MB, 2 800 K floppy drives
We are talking pure Plus power now. The 4 MB RAM opens some new doors... It is possible now to make a 2 MB Ram Disk and have the operating system and applications run on that. This means that you can put a pretty well filled system folder next two 'modern' apps on the Ram disk and still have 500 K or so on it left.... For the occasional large Clipboard file. When using a 2000 K RAM disk in combination with a 500 K RAM using system you'll have about 1500 K of Ram left for running applications, games etc. More than enough for most programs.
In order to build, use and boot form a RAM disk, you'll need a shareware control panel called RAMdisk 3.23+. If you put that in the system folder you can configure your plus to load at startup the contents of one or two floppy's automatically two a RAM disk, then have the Plus automatically boot up from that RAM disk and after that also automaticaly eject the floppy's in order to free the floppy drives, leaving 1600 K space to store documents or additional applications. The advantage of this setup is that you'll not only have a staggering 3600 K of disk space, but also a even more silent Plus (when you put the system folder and programs on the RAMdisk, you won't hear any floppy drive noises when the machine needs to access the system folder or program). Besides your Plus will become faster too because RAM is much faster storage than floppy disks and even hard disks.
When using a RAM disk you can fill the whole 800 K system floppy disk with all sorts of gadgets like a space consuming inkjet printer driver or appleshare software (45 K) in order to connect with your file server. Luxury items like 'Date', 'Popchar' and 'Superclock' are also possible now. You might wanna add the driver of your Zip also, adding yet another 100 MB disk space to your Plus.

System 6.05 Setup
A 2000 K RAM disk filled with the contents of:
ONE floppy with one system folder containing:
AppleShare 45 K
AppleShare Prep 1 K
AutoIdle 10 K (a small screensaver is very healthy for a Compact Mac)
Backgrounder 5 K (for background printing)
Clipboard File 1 K
Date 11 K
Finder 108K
General 14 K
LaserWriter prep 28 K
LaserWriter 64 K
Multifinder 50 K
Popchar 23 K
Print Monitor 37 K
RamDisk+ 54 K
Super Clock 9 K
Startup finder 1 K
System 212 K (all unnecesary fonts and da's have been removed)
Total: 673 K, leaving ca. 127 K free for more gadgets

AND a SECOND floppy containing:
'Advanced' drawing program 341 K
'Advanced' word processor 347 K
Conversion filters 63 K (making you compatible with the rest of the world)
T otal: 751 K, leaving ca .49 K free on the floppy drive for conversion filters etc....

After automatically loading the system floppy (673K) and the Application floppy (688K) on the 2000 K RAM disk, we will still have 576 K free.

Links

An interesting page about floppy driven Plus being used for email, can be found here

You can also find info about floppy driven Macs (SE and LC) on: They might be giants.