I have been using the Google Cloud Storage Manager
link on the Google APIs console in order to upload my files.
This works great for most files: 1KB, 10
The web UI only supports uploads smaller than 2^32 bytes (4 GigaBytes). I believe this is a javascript limitation.
If you need to transfer many or large files consider using gsutil:
gsutil -m cp /path/to/*thousands-of-files* gs://my-bucket/*