stat -c '%w' file on filesystems that store creation time.
Note that on Linux this requires coreutils 8.31, glibc 2.28 and kernel version 4.11 or newer.
The POSIX standard only defines three distinct timestamps to be stored for each file: the time of last data access, the time of last data modification, and the time the file status last changed.
Modern Linux filesystems, such as ext4, Btrfs, XFS (v5 and later) and JFS, do store the file creation time (aka birth time), but use different names for the field in question (crtime in ext4/XFS, otime in Btrfs and JFS). Linux provides the statx(2) system call interface for retrieving the file birth time for filesystems that support it since kernel version 4.11. (So even when creation time support has been added to a filesystem, some deployed kernels have not immediately supported it, even after adding nominal support for that filesystem version, e.g., XFS v5.)
As Craig Sanders and Mohsen Pahlevanzadeh pointed out, stat does support the %w and %W format specifiers for displaying the file birth time (in human readable format and in seconds since Epoch respectively) prior to coreutils version 8.31. However, coreutils stat uses the statx() system call where available to retrieve the birth time only since version 8.31.
Prior to coreutils version 8.31 stat accessed the birth time via the get_stat_birthtime() provided by gnulib (in lib/stat-time.h), which gets the birth time from the st_birthtime and st_birthtimensec fields of the stat structure returned by the stat() system call. While for instance BSD systems (and in extension OS X) provide st_birthtime via stat, Linux does not. This is why stat -c '%w' file outputs - (indicating an unknown creation time) on Linux prior to coreutils 8.31 even for filesystems which do store the creation time internally.
As Stephane Chazelas points out, some filesystems, such as ntfs-3g, expose the file creation times via extended file attributes.
Renaming does update the Change time:
$ mkdir tmp
$ cd tmp
$ echo abc > a
$ stat a
File: `a'
Size: 4 Blocks: 8 IO Block: 4096 regular file
Device: 26h/38d Inode: 5038682 Links: 1
Access: (0664/-rw-rw-r--) Uid: ( 1000 / zelda Gid: ( 1000/ zelda)
Access: 2013-12-12 07:06:58.981107444 +0100
Modify: 2013-12-12 07:06:58.981107444 +0100
Change: 2013-12-12 07:06:58.981107444 +0100
Birth: -
$ mv a b
$ stat b
File: `b'
Size: 4 Blocks: 8 IO Block: 4096 regular file
Device: 26h/38d Inode: 5038682 Links: 1
Access: (0664/-rw-rw-r--) Uid: ( 1000/ zelda) Gid: ( 1000/ zelda)
Access: 2013-12-12 07:06:58.981107444 +0100
Modify: 2013-12-12 07:06:58.981107444 +0100
Change: 2013-12-12 07:07:14.893238472 +0100
Birth: -
The Access time is updated when reading the contents of a file. Modify when you actually update the file (opening for modification is not enough to change Modify time).
Best Answer
You cannot change the ctime by ordinary means. This is by design: the ctime is always updated to the current when you change any of the file's metadata, and there is no way to impose a different ctime. To change the ctime of a file, you need to do one of the following:
debugfs) and twiddle the bits on the disk (don't do it while the filesystem is mounted).