Dataloader.io

Link	http://dataloader.io
Pricing	FREE for 10,000 records per month
Description	Just the best data loading tool for Salesforce, unfortunately you eat through your 10k records too quickly

Documentation

Only basic documentation and basic community support in the free version

If things are failing or triggering lots of errors in your org on Import or Update use Batch API and set the number of records per batch to much lower, and it should work. Thank you to @salefixjason for rescuing me on this one - that was a bad Salesforce day.
You can't export from Professional Edition without the API - as you can only use the Bulk API for export. This is a strange limitation.