alanback: When I used to play at Vog they had an Auto-roll switch which was very useful. This was the case even though these were live matches. When you thought the game was moving into a phase where you might like to double then you'd switch off the auto-roll and take it a bit more slowly. On a turn-based site, especially against opponents who take 7 days per move, taking it a bit more slowly isn't the best default!
One disadvantage, though, is that automatic rolliing removes the opportunity for skilled psychokinetic dice rollers to concentrate on getting the dice that they need.
playBunny: The protoype of all internet backgammon servers, FIBS (First Internet Backgammon Server) has always had several software toggles, including toggle double. With doubling toggled off, the dice are rolled automatically each turn. Another useful setting is toggle greedy, which if set on will cause the server to automatically bear off the maximum number of checkers in unambiguous situations.