With version 4.0 of DSL, the system boots into an X desktop running the JWM window manager, but you can select the original window manager (Fluxbox) or the alternate SWM (Small Window Manager) from the main DSL menu. I preferred Fluxbox for its right-click-on-the-desktop context menu that provides just about all the most important options in one place.
Few of the larger productivity apps are included by default as a space-saving measure -- Firefox is here, for instance, but none of the OpenOffice apps or even AbiWord. However, DSL includes an extension mechanism called MyDSL, where you can browse a file repository, either the online repository or one on a local disk, and install many of the programs you'd find in other distributions. I added AbiWord 2.0.1 this way without much difficulty.
Like some of the other distributions here, you can install DSL to a hard drive in one of two ways. The most broadly supported method involves writing a disk image to a file on the hard drive and booting that -- essentially booting a version of the live CD directly from the hard drive. It's also possible to perform a more conventional Debian-style installation, or take the existing install and re-burn it to a whole new CD from within DSL. A third option is to save the modules you want to use to a directory named mydsl on an external media (a hard drive partition or USB flash drive) and point DSL at that device when booting by passing a parameter.
The granddaddy of many a tiny distribution, Knoppix is also the original boot-and-go distro, and has been well-maintained for a long time.
Not quite the first live CD, but certainly the one that has come to define the state of the art, Knoppix is also the source for many slim-and-trim distributions.
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Knoppix was one of the first of the Linux live CD distributions. Since its emergence in 2003, Knoppix has more or less become the reference point for other live Linuxes. It isn't quite as tiny as the other mini-distros described here (the CD ISO is 713 Mbytes) but to not talk about it here seems like an omission, since a number of other slimmed-down distributions have been based on it and owe it a debt.
Knoppix actually comes in "mini" and "maxi" editions -- the "mini" being the 713-Mbyte ISO with a relatively small set of components, and the "maxi" being a full 4-Gbyte DVD image which unpacks to over 9 Gbytes of files. For most people the CD-sized image should more than do the trick, since it includes plenty of popular packages -- Firefox and Thunderbird (in their rebranded incarnations, Iceweasel and Icedove), OpenOffice, the Scribus desktop publishing app, GIMP, Java support, Wine, and tons more.
The default desktop environment in Knoppix is KDE, which may be a bit heavy for those with minimal RAM, but it seemed to perform acceptably well on the 128 Mbytes I tested with, and you can always switch to FluxBox or one of the other low-impact desktops if you want. KDE's menus also come pre-loaded with shortcuts to both the applications and a whole bevy of system-configuration scripts -- wireless setup, setting the password for the root account, even configuring a TV tuner card if one is present. FluxBox and IceWM have different application bundles available through their menus, though, so be warned that what shows up in one window manager's menus doesn't always appear in another.
The standard way to run Knoppix is directly from the CD or DVD. If you want to run Knoppix entirely in RAM, you'll need around 1 Gbyte of RAM to pull that off. Another caveat -- one which is stressed very strongly in the Knoppix wiki -- is that installing Knoppix to a hard drive is not always dependable, simply because Knoppix has been designed to run as a live distro. It can be done if you are careful and do some homework ahead of time about what variables are involved, but it isn't recommended for beginners. (Other distributions based on Knoppix, however, may behave differently.)
As far as saving data persistently, what Knoppix does offer is the ability to save the user's documents and preferences in a disk image that can be stored somewhere other than the CD -- a flash drive, a hard disk partition, etc. Said image can also be AES-256 encrypted for security, so someone who doesn't have the password won't be able to simply mount it and read it.