The PS3 is only able to recognize hard drives formatted in the FAT32 format. NTFS, and any other format type out there is completely unusable by the PS3. Since pretty much all PC systems out there today use an NTFS formatting, it is likely not going to be readable on the PS3.
I'm having to overhaul my PC due to hard drive failure problems. In the meantime, I'd like to continue to have access to my media on my external hard drive.
I have a wireless D-Link router that has a USB connection. Can I connect the external hard drive by this USB connection on the router and have the PS3 recognize the hard drive??
Kind of. If what you're interested in is photos, videos and music, many of the new routers provide DLNA support for attached hard drives. And even if yours doesn't, there may be 3rd party firmware available that does . . . OpenWRT and dd-wrt are two that come to mind that provide DLNA support. Note that having the drive formatted in NTFS may not work when router-attached, but FAT32 does (although other file systems such as ext3 generally provide better performance).
If you're planning to use the router-attached hard drive for PS3 backups, though, that won't be possible.