Yes! For data from Cycle 5 onwards data-files can be downloaded individually from the Request Handler. Search for your data on https://almascience.org/aq, select the data you are interested in, click on 'Submit download request' and then use the small triangles in front of the '*auxiliary.tar' and/or '*001_of_001.tar' files to get access to the individual files. These can be either selected for download via the checkbox or you can use the browser's right-click and 'Save as ...' to download the file through the browser.
For Cycles 1 to 4, it is only possible to download data in raw ASDM tar files or processed data tar file packages.
For Cycle 1+ data, all images are contained in a relatively small single file ending with 001_of_001.tar. The other files (ending with asdm.smd.tar) contain the raw data.
For Cycle 0, in order to easily find which tar files contain the actual images, this page has been created. Also, the externally developed package astroquery can be used to download Cycle 0 tar files and extract the FITS files.
Archive data products are described in How are ALMA data products packaged?.