Recently I got into a situation where vmware was not booting a VM, and I had some important files on the VM disk.

The commands which worked successfully are :

vmware-mount -p /path/to/file.vmdk

which gave the output:

[AppLoader] Use shipped Linux kernel AIO access library.
An up-to-date "libaio" or "libaio1" package from your system is preferred.
Nr      Start       Size Type Id Sytem                   
-- ---------- ---------- ---- -- ------------------------
 1       2048     974848 BIOS 83 Linux
 2     976896    3905536 BIOS 82 Linux swap
 3    4882432   79001600 BIOS 83 Linux

Partition 3 was of my interest. To mount it run the following command.

vmware-mount  /path/to/file.vmdk PARTITION_NUMBER /path/to.mount/to

which in my case became!

vmware-mount  /path/to/file.vmdk 3 /mnt/vmdk