In my local MAMP site I'm not able to upload any files.

Gives me this error in Chrome:

This error in Safari

"Failed to load a resource: The network connection was lost."

Things I did

• I've checked the asset folder path
• makes sure folder is writable
• nothing strange in the craft.log
That usually means "something fatal happened" when trying to upload the file. The usual culprits are the php.ini max_execution_time and memory_limit settings, but if it's happening for small files too, something else could be going on.
Check if you have a craft/storage/runtime/logs/phperrors.log file. Any PHP fatal errors will be logged there. If not, then check the Apache error logs to see if it's an Apache problem.