Only a few Commodore computer were able to work without any additional equipment, like the "all-in-one" SX-64 (sometimes called also Executive 64), a Commodore 64 compatible portable computer with one 1541-alike floppy drive and a
5 inch color monitor.
Most of the other ones have to use at least a monitor, many of them also additional equipment like the floppy drive, a memory cartridge, a printer or trivial accessories like a joystick or an external reset switch.
A famous 3rd party equipment for example is CMD's FD-2000 floppy drive with JiffyDOS, this drive is the ultimate weapon for handling real
3.5" floppies (6336 blocks free):
Many web sites offer additional infos or even the internal used disk format or special tools.
Also, there are still some recently developed new equipment:
The 1541 Ultimate - a silicon version of the 1541 drive (and even much more like a RAM expansion unit, a 6502 kernal implemented with a Xilinx Spartan make this possible):
It works even with DOS/65, which is an operating system also for the Commodore 64 similar to CP/M 2.2, but without a 8080 or Z80 cpu:
More info about the '1541 Ultimate' can be found here.
Similar hardware based drive emulators (but somewhat more limited) are the 1541-III (PIC based) and MMC2IEC (Atmel ATMega32 based).
An updated device (2009) comes from Jim Brain named uIEC/SD, see news entry at Commodore Homestead. General infos about it can be found on the C64 Wiki. Unfortunately I have not seen it "in action" with photos (may be someone send me a photo?).
Also, there is a promising new developed hardware called 'xum1541', an USB device (based on an Atmel AT90USBKEY developer kit at the moment) which connects a PC with a 15x1 drive via USB with the help of an XAP1541 adapter. New: Now with nibbler support !
If you own a (spare) PC, you will be able to emulate a 1541 also:
There is 64HDD which will give you the ability to emulate a even bigger floppy drive/harddisk and this will work with a 32-Bit Windows OS.
1541EMU is another software project to emulate a drive under MS-DOS.
If you are a Linux fan, try 64Net/2, another sourceforge project.
You should not mistake these software projects with the ability to transfer disk images to a real drive, this can be done with the help of OpenCBM or StarCommander.