How to copy photos Mac-Mac, and back up for long term?

Take a look at this article on how to backup your data: http://support.apple.com/kb/HT1553

A locally connected external hard drive on each system would be my first thought. It is the easiest to put in place and doesn't put all your eggs in one basket should a drive failure occur.

For your home computer and perhaps the work computer (assuming it is running 10.5.8 / 10.6.4), you can use Time Machine to do the backups for you.

If you would like another layer of backups on top of the external drive you can use the MobileMe backup program to do the backups to CD / DVD.

Hope that helps.

Time Capsule is a great solution if you have a house full of computers or a portable computer that is not kept on a desk. It allows for multiple computers to backup using Time Machine over the network.

For the setup you indicated I would probably go for a locally connected USB or Firewire external drive (Firewire is nice for the speed and also if you ever decide to use the drive for editing video.)

Choosing a brand that has a long history of making drives is a good idea. Also take a close look at the details for the drive to see what kind of warranty it has. Most drives come with a 1 year warranty, some even longer.

Drives that I have currently running for over a year:
LaCie
Seagate
Western Digital

When choosing a backup drive I pick ones that are at least twice the size of the drive I'm backing up. So if the internal drive of my system is 320 GB I get a 640 GB (Usually just round up to a 1 TB). This gives you room to grow.

As you have unfortunately experienced, drives crash. I would be willing to argue that all hard drives will eventually die. Thats the nature of any device that has moving parts. It wears down over time. No matter what kind / brand of drives you decide to go for, just keep in mind that at some point down the road you may need to replace it.

Happy shopping!

If you want the external hard drive just for Time Machine backups there are number of possibilities. As MadisonP suggested the Time Capsule is one. I use Otherworld Computing's OWC Mercury Elite-AL Pro, 1.0TB, FireWire 800/400, USB 2.0, eSATA drive. I've had very good luck with their drives. A variety of sizes are available all the up to 2 TB.

OT

TIP: For insurance against the iPhoto database corruption that many users have experienced I recommend making a backup copy of the Library6.iPhoto (iPhoto.Library for iPhoto 5 and earlier versions) database file and keep it current. If problems crop up where iPhoto suddenly can't see any photos or thinks there are no photos in the library, replacing the working Library6.iPhoto file with the backup will often get the library back. By keeping it current I mean backup after each import and/or any serious editing or work on books, slideshows, calendars, cards, etc. That insures that if a problem pops up and you do need to replace the database file, you'll retain all those efforts. It doesn't take long to make the backup and it's good insurance.
I've created an Automator workflow application (requires Tiger or later), iPhoto dB File Backup, that will copy the selected Library6.iPhoto file from your iPhoto Library folder to the Pictures folder, replacing any previous version of it. There are versions that are compatible with iPhoto 5, 6, 7 and 8 libraries and Tiger and Leopard. Just put the application in the Dock and click on it whenever you want to backup the dB file. iPhoto does not have to be closed to run the application, just idle. You can download it at Toad's Cellar. Be sure to read the Read Me pdf file.

NOTE: The new rebuild option in iPhoto 09 (v. 8.0.2), Rebuild the iPhoto Library Database from automatic backup" makes this tip obsolete.