I sometimes see tasks that are still being processed even though the deadline expired several days ago. Is it still useful for such tasks to run? If not, why doesn't the system automatically stop/delete them?

You can easily return work after the deadline, and as long as you're first to return it before the next person who got a replacement task sent, get credit for it. Some projects don't even adhere to the deadline, with massive models being calculated, such as ClimatePrediction.net. They give work out with a far-away deadline, but it happens that that deadline isn't even reached. Then it's useful that BOINC continues afterwards.

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I may be wrong but I think some projects abort tasks when they pass the deadline. It is be done from the server side I think.

With CPDN the reason for still setting a deadline that isn't used is that the BONC server code requires it. There was also the issue of how it would play with other projects if a much shorter deadline was used. There has been some discussion on the CPDN fora about shortening the deadlines as a lot of the work these days is requested byPhD students at various universities around the world who have deadlines that would not be met for example by my crunching tasks on my ageing netbook. Another reason for the very long deadlines is historical in that tasks used to take several months (often six or more) even on fast machines for the day.

Thank you for your replies.

I'll just let the tasks continue then, instead of deleting them when I happen to see them.

Some projects have a buffer that allow tasks to return after the initial deadline. Others can extend the deadline of tasks if the client is still communicating with the server. The deadline is only updated on the server and not on a users client. RNA is one project I know that does this.