<p>I work with a lot of offsite developers and contractors. I ask them daily to send me a quick 5 minute status of their work for the day. I have to sometimes consolidate the status of individuals into teams and sometimes consolidate the status of a week, for end-of-period reporting to my clients.</p>
I want to learn:
<ul>
<li>Items accomplished and how much time was spent on each</li>
<li>Problems encountered and how much time was spent on each</li>
<li>Items that will be worked on next, their estimates (in man hours) and their target dates</li>
<li>Questions they have on the work</li>
</ul>
I'm looking for a format that will provide this information while:
<ul>
<li>Being quick for the developers to complete (5-10 minutes, without thinking too much)</li>
<li>Easy for me to read and browse quickly</li>
<li>Is uniform for each developer</li>
</ul>
<p>What would you suggest?</p>

Just give them a template laid out in a format that you expect to see the data returned in.  You may also consider increasing the time they are going to devote to this and removing the "not thinking too much" clause if you are requiring estimates for future work. I wouldn't trust an estimate that someone came up with in 5 mins. without thinking.
If you are currently using any project management software, it should be trivial for the developers to record and review (or even just remember) what they have done compile it for you.  Ideally they would be recording issues or questions throughout the day and not trying to come up with them just to fill in the report.
It seems like your "I want to learn" list is an excellent starting point to generate a template from. Only you will know what the perfect format for you is.