MongoDB optimization on high data
First, let me say that with the information given it will be hard to get at the root cause - it is usually an iterative process that takes multiple attempts to track down the culprit.  In the interest of answering your "what next?" portion of the question rather than identifying the root cause, read on.....

First, a couple of recommendations:


Get the host into MMS (it's free) - see http://mms.10gen.com - so you can graph stats over time and get a view of the issues without having to be sitting on the box running commands
Get munin-node installed too, so you can correlate ops etc. with IO (install docs for MMS explain this).


Next, a couple of quick checks for common causes:


What is your filesystem/kernel? - these generally need to be ext4/XFS and recent enough to have fallocate working (2.6.23 and 2.6.25 respectively) so that new file allocation is not slow
Assuming you don't get MMS and munin installed, get iostat output to match up with mongostat to determine if IO is the root cause for the bottleneck
Do you do any periodic batch updates that grow the documents significantly (i.e. that would cause moves)?  Moves are expensive and can cause IO to get backed up
Is your disk up to the data volume you are writing to it?  MongoDB fsyncs to disk every 60 seconds by default, if the volume that needs to be synced after 60 seconds is massive (say because of an insert spike) then you can also run into issues


That's not an exhaustive list, I have seen other issues cause this, but that should get you started down the right path.