Is it possible to use Time Machine to back up to an external hard drive connected to a Mac on same wifi network?
Yes. I've been doing this since Snow Leopard. All my MacBook Pros in the house do their Time Machine backups to an external USB drive that's hanging off an iMac running the standard OS X install (i.e. not Server). At the time of writing the iMac has been upgraded to Lion as has one of the MacBook Pros.
First, configure your target machine (the one with the USB drive attached):
Now you need to configure your source machine (the one you want to keep it's Time Machine volume on this drive):
You're now all set up to use this remote drive as your Time Machine backup location. When Time Machine runs you'll see this drive appear as a mount on your system, and when it's done the mount will go away.
If you browse this drive from the target machine you'll see sparsebundle files, one for each machine that's doing a Time Machine backup to this drive, on the disk. These are the actual "disks" that Time Machine is using on each machine to keep the incrementals. If you click on one, it should mount and you should be able to browse it like normal.
If you have a complete disaster and need to do a fresh OS X install and recover from Time Machine you can point the recovery process at the remote drive and it will ask you to pick a sparsebundle from the drive to recover from. Or, and this is what I recommend, you can unattach the drive from your target and attach it via USB to your machine and do the restore over USB which is much faster.
I can confirm that complete restores from Time Machine backups kept in this manner work well. I've had to do two of them in the past few years on machines that keep their backups this way and both went smashingly well. Browsing Time Machine history in the Time Machine viewer can be a bit laggy, but it does work.
The answer by Ian C. is correct. However, one small (but important) detail has been overlooked (one that took me a good hour to figure out!).
If the drive is not showing up in Time Machine on your Source Machine (the machine you want to back up), do the following:
Now go back to your Source Machine and your External Drive should show up in the list of Time Machine Backup Disks!
If the Mac is running OS X Server (In 10.7, not sure if this is available for 10.6) then you can turn on Time Machine Server, which does exactly what you need. There's no need to run any of the other server tools if you don't want. this is the only officially supported way to do this that I know of.
If your backups are really important and you need a much more stable system for doing backups either remotely, wirelessly, online or an external drive, then I describe the best way how to do this below.
A hard drive used for Time Machine backups requires an HFS+ journaled partition which gets corrupted and unmountable very easily. Your signal getting cut off, a cable getting detached, the power going off, or your computer crashing during a backup is all it could take to have big problems. Often Disk Utility cannot repair the disk and you lose all your stored data.
This is why using Time Machine over wireless is risky (time capsules are expensive but do seem to be more reliable); be really sure that you have a good, reliable WiFi signal and set up your router to use a channel different than any other WiFi sources. (The free program WiFi Scanner is great for analyzing WiFi interference.)
My backup hard drive had a habit of mysteriously disconnecting without properly ejecting numerous times and I have lost files; most of my video, graphics, and photos which take up more storage then my laptop can hold.
I do video editing and design and for my situation I need something more reliable and flexible. It's worth it to me to spend a little extra money on this software because losing data had cost me in more ways than one. Here is an excerpt from their website:
I use xTwin with an external USB teradrive. HFS+ Journaled formatting is so easy to corrupt and lose your data with but Time Machine requires it. So far the best solution I believe is to use xTwin with NFTS formatted drive. I learned that NFTS is much more stable and a lot easier to do data recovery with. Disk Utility does not come standard with this format, but you can get software such as Paragon which adds this option into disk utility. It is much more important to me to have reliable backups than versions and the cool time machine way of accessing older files.
I will stick with this until Apple proves they have made a more stable filing system for backups.
I had the same issue with TM not recognizing/mounting a TM-formatted NAS volume. After 2 days of reading forums and tinkering, my solution was a variation on the SMB - AFP issue. As I have not seen my issue & solution explained elsewhere, I am posting it here.
Running 10.7.5 on a MBA. Backup destination is a Synology DS214play, running DSM 5.0 with native TM-support.
We also have Mac Mini's running 10.6 and the process for pointing TM to the Synology NAS was very straight-forward which ruled out a problem with the Synology NAS. This was the major source of confusion. The different OS versions seem to create a subtle, but crucial difference in how TM handles this.
On the MBA (10.7.5), mounting the drive through finder and setting it to always re-mount during start-up was straight-forward. I paid attention to the SMB / AFP formats when setting everything up on the partition on the NAS. When mounting the drive on the MBA, it recognizes and displays only the drive name ("DiskStation"). In the background, it was defaulting to an smb format despite me having specified the afp format on the destination drive.
Solution: instead of selecting and mounting the drive with a mouse-click, manually enter the IP address of the destination with an afp-prefix. TM then instantly recognized the destination volume. Somewhere between 10.6 and 10.7.5 something was changed causing TM to default to adding an SMB-prefix to the destination volume. Tricky because it is then hidden. Hope this helps.
It works even though Apple support told me it wouldn't.
Important step that I missed:
Open Finder on the machine to be backed up. Find your target machine and click on it. MOUNT the drive on this machine—i.e. make sure that the back up drive on is visible on your Finder sidebar as a separate entity (File Add to Sidebar).
I also portioned my backup Mac with a 500G partition for the backup to ensure no corruption etc. on the backup Mac with other applications.
Not possible that I know.
Only if connected to AEBS (Airport Extreme Base Station) or server as far as I know