For our online/voip games, I keep duplicate record sheets for each of the PCs in our game. Some of my note taking during sessions is recorded directly onto these sheets, such as the actual value or nature of magic items. I find this to be helpful in other ways - I don't have to ask the players for information about their inventory or attributes to make rulings, and I can update their items as we play (while they do) so we're on the same page.
I think this came about because we couldn't easily exchange the sheets - I didn't want to force the record sheet to be a text file continually being edited instead of the usual pencil and paper. Even if it was a text file, having to re-save and file transfer it slows the game a little. So we have this duplicate records method. As DM in our S&W games I use index cards as record sheets. These work really well since there's not as much shuffling and hunting for the right one when needed. I like the tangibility of these records too, as opposed to something stored on disk. Like using miniatures that aren't strictly required, their physical presence still contributes something to the game.
I don't keep duplicate sheets for face to face games, but I wonder if others do... For large groups this might slow the game with too many records to keep track of, but maybe not so much with index cards. I never played this way as a kid, but in retrospect maybe I should have. At that age, it seems like there was always sloppy record keeping and even the occasional cheat that got busted. Cheating at D&D! The very idea. I’ll never forget Willie showing up that day with the Wand of Orcus from who knows where.
I'm also curious as to whether most DMs hold onto the record sheets of their players between sessions or whether the players bring them to the game. I wonder if the DM holding them slightly breaks down trust or the players' sense of character ownership. Back in the day, it seems like my friends and I held onto our own records and our characters might move from one DM's game to another. Rules discrepancy wasn't an issue, since we didn’t have many house rules, if any, and the AD&D books were law. Nowadays I imagine most DMs hold onto these records for their players between sessions just for the sake of convenience.
Perhaps this reflects a subtle shift in how we’ve come to view the game having grown older. The last time I played with my nephew Josiah I thought I saw a little reluctance to turn over his character sheet. I ended up keeping it for fear it would be lost. He got to walk away with his own set of dice, so at least he owns the means of determining his character’s fate (he ended up losing some of the dice though.) Maybe I should have had him keep it, and if he lost it, well, his elf got lost and died. Or else he's fallen into a magic sleep until found and woken up. Hey kid, that paper is someone's life!
When we hold on to the only physical manifestation of our character, the record sheet, when we feel we “own” it and the character, I believe we’re more strongly in the shared, imaginary game space. Being willing to turn it over or give control of your character to the DM or other players may simply be a matter of maturity, but I also think how easy we find it to relinquish that control is a barometer of how immersed in the game we really are.