Most of the time, mount is the most convenient method. For a complete and exact list of currently mounted filesystems, you should read the contents of /proc/mounts (e.g., with cat /proc/mounts).
For example, if mounting / readwrite failed and it was then mounted readonly as a fallback, /etc/mtab (which the mount command reads from to tell you what's mounted, and writes to--if it can--when it changes what is mounted) would not be updated to reflect that / (which contains /etc/mtab) is currently mounted readonly. In this situation, running mount would typically tell you (incorrectly) that / was mounted readwrite.
Under normal conditions (i.e., when the filesystem that contains it can be written to), /etc/mtab contains a list of currently mounted filesystems. This is not to be confused with /etc/fstab, which contains a list of filesystems that are supposed to get mounted automatically when the system starts up.
Of course, if the /proc virtual filesystem is itself not mounted, then you cannot read any of the virtual files in it, which would include /proc/mounts. This very rarely is the case. In this situation, mount is probably your best option for seeing what's mounted.