Depends from the filesystem.
ext4 now support up to 1 exbibyte and files with sizes up to 16 TiB.

For XFS the following limits are valid:
For Linux 2.4, 2 TB. For Linux 2.6 and beyond, when using 64 bit addressing in the block devices layer (CONFIG_LBD) and a 64 bit platform, filesystem size limit increases to 9 million terabytes (or the device limits). For these later kernels on 32 bit platforms, 16TB is the current limit even with 64 bit addressing enabled in the block layer.