Delta poses an interesting question about who keeps character sheets – the DM or the player. There are pros and cons to either approach, although personally I lean towards letting the players keep their own character sheets. When I’m a DM, I always keep a one-page summary of all the PCs and their essential stats for use during games, so the physical sheet is not that important to me.
However, it is possible to get the best of both worlds using shared documents (Google docs is the one I use, but not the only solution available). Since most of our group’s gaming happens online, this works great – but you can use shared documents for face-to-face gaming as well, players can update their own shared character sheet before each session and print it out if they want a hard-copy to doodle on. If you just use a text document, no setup is needed, other than for the DM to allow both himself and the player to edit the shared document (easy to do in Google docs under the ‘share’ menu option for an individual document). You can allow as many or as few people you like to view or edit each shared document. I like to add a bit more structure to the character sheets. Here is an example, this shared Google doc character sheet is for 3LBB OD&D.
For both sheets I used the ‘Get shareable link’ menu option in my Google drive, by default this allows anyone with the link to view the document, but not edit it. A player could use that option to share his own sheet with the DM, if he was reluctant to allow edit access. When starting my own games, I just provide the links to a blank character sheet (already in my drive) to each player, and let them edit it as needed.