Q. Does any Linux distribution support suspend or hibernate functionality?
A. Yes, almost all modern Linux distribution supports suspend or hibernate functionality. In the Linux kernel, Hibernate or suspend-to-disk, suspend-to-ram, suspend-to-file is implemented by swsusp which is built into the 2.6 series.
Hibernate is a feature where the contents of RAM is written to the hard disk (as either a file or on a separate partition) before powering off the system. Later the system can be restored to the state it was in when hibernation was invoked, so that programs can continue executing as if nothing happened. Hibernating and restoring from hibernate is also generally faster than a hard reboot and, if necessary, can be done without user interaction.
I've personally tested following distributions:
+ Red Hat Enterprise Linux 5 ( desktop edition )
+ Debian Linux
+ Fedora Linux
+ Ubuntu Linux
How to suspend and hibernate a laptop under Linux
=> Click on Shutdown > Select Suspend or Hibernate as per requirement.