All my tasks, as they complete, enter the state "Uploading (suspended - user request)" and get stuck there. The project is in the state "Scheduler request pending, Requested by user".
Restarting BOINC and rebooting the system have no effect.
I've run BOINC without incident for many months; this seemed to appear out of the blue.
Now all tasks are in this state, so no further work can take place.

No change when I try the following:
* In the Tasks pane, select a task; third button says "Suspend". Click that, then click Resume.
* In the Projects pane, select the project, Suspend, Resume.
* In the menu bar, "Activity>Run Always" or "Activity>Run base on preferences"
* Upgrade BOINC to 7.2.42

Now what?
It appears the task uploads are not suspended by any user controls I know of.
Preferences: Network: Max download =0, Max upload =0, transfer at most 0 MB every 0 days, min buffer 1 day, max additional 1 day, no boxes checked.
Platform is OSX 10.6.8 (Snow Leopard), MacBook Air (late 2010).
Network connectivity is normal.
Disk pane shows plenty of space available to BOINC.
I run only one project, World Community Grid. (Tasks are FightAIDS@Home and Mapping Cancer Markers.)

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All my tasks, as they complete, enter the state "Uploading (suspended - user request)" and get stuck there. The project is in the state "Scheduler request pending, Requested by user".

* In the menu bar, "Activity>Run Always" or "Activity>Run base on preferences"

That is the 'Computing' Activity selector, your tasks compute O.K, the problem is your tasks aren't being allowed to upload, and Boinc isn't allowed to do scheduler contacts,

So, what happens if you set 'Network activity always available'? or Network activity based on preferences? Instead of Network activity suspended?

Claggy

You mention the Tasks pane, the Projects pane, and the Disk pane.

Did you happen to pass by the Transfers pane? That's where information about uploads will be found.

Yes, the culprit was cc_config.xml unsigned_apps_ok! Restoring it to 0 from 1 and restarting BOINC caused my tasks to upload normally.
I'm confident I did not set that variable to 1 myself; strange.