I believe Jean Todt suggested this a while ago. It came with the suggestion that drivers have large, easy-to-identify numbers on their cars so that fans could pick their favourite drivers out (since it can be a little hard to pick drivers out based on helmet designs and camera mountings). The idea was modelled on MotoGP, where riders are issued a number when they enter a sport, and that number stays with them for the rest of their career - so Valentino Rossi will always be #46, and Marco Simoncelli will always be #58. The only time the number would change would be when a driver is World Champion, in which case he adopts the #1 and his normal racing number is put in escrow (so it can't be issued to/taken by another driver).
Of course, the teams will offer resistance for two reasons: firstly, numbers are assigned based on championship position; the better they do, the lower the number they get, so it's something of a status symbol. And secondly, it would take up advertising space. McLaren and Mercedes are the only teams that really show their numbers on the rear wing, and Hispania is the only team that has clearly-visible numbers. Most of the others keep their numbers on the vertical upright alongside the sidepods, and some - most notably Force India and Team Fernandes - have put their numbers in some pretty questionable places (Force India put theirs in the gap between the front wing struts, making it virtually impossible to read the number short of standing on top of the car; Team Fernandes used to put theirs right at the end of the sidepods). They'd probably leave the numbers off if they could, but it's compulsory.
Of course, if personalised numbering went ahead, there's a few difficulties on hand: first of all, what happens if two drivers want the same number? 17 is a signifcant number for me, but what if another drivers wants the same number because it's significant to them? How do you go assigning numbers fairly? And secondly, what do you do when there is a particularly famous number that becomes available? Like the number 27 - a lot of famous drivers have raced with it. Or let's say that Ayrton Senna always raced with the number 99 - you drivers might want that number specifically because it was Senna's and a lot of young drivers were influenced by him. In the NHL, teams can choose to retire a number when a famous player leaves; the Edmonton Oilers did it when Wayne Gretzky retired. So I suppose you could retire a racing number for a decade (Formula 1 won't see a hundred drivers in ten years) as a mark of respect once a driver leaves.