Can you upgrade from Os x 10.4 to 10.5 or higher?

Possibly. Depends on what specific computer model you have, but you haven't provided any such information.

So we know more about it...

At the Apple Icon at top left>About this Mac, report the version of OSX from that window, then click on More Info, then click on Hardware> and report this upto but not including the Serial#...

Hardware Overview:

Model Name: eMac

Model Identifier: PowerMac6,4

Processor Name: PowerPC G4 (1.2)

Processor Speed: 1.42 GHz

Number Of CPUs: 1

L2 Cache (per CPU): 512 KB

Memory: 2 GB

Bus Speed: 167 MHz

Boot ROM Version: 4.9.2f1

The absolute highest any G4 can go is...

Leopard requirements/10.5.x...

* Mac computer with an Intel, PowerPC G5, or PowerPC G4 (867MHz or faster) processor

minimum system requirements

* 512MB of memory (I say 1.5GB for PPC at least, 2-3GB minimum for IntelMacs)

* DVD drive for installation

* 9GB of available disk space (I say 30GB at least)

Classic/OS9 Apps no longer supported.

Trouble is Apple no longer sells it, check eBay & such for the Retail version, not the Gray Discs...

http://www.ebay.com/sch/i.html?_nkw=mac+os+x+leopard+retail+10.5

Because you have a Core Duo model you are limited to Snow Leopard. You already have the maximum RAM for your model. All you need do is purchase the Snow Leopard DVD from Apple's Online Store - $29.00.

How to Install OS X Updates Successfully

A. Repair the Hard Drive and Permissions:

Boot from your current OS X Installer disc. After the installer loads select your language and click on the Continue button. Then select Disk Utility from the Utilities menu. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer. Now restart normally.

If DU reports errors it cannot fix, then you will need Disk Warrior (4.0 for Tiger) and/or TechTool Pro (4.5.2 for Tiger) to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X.

B. Make a Bootable Backup Using Restore Option of Disk Utility:

1. Open Disk Utility from the Utilities folder.
2. Select the destination volume from the left side list.
3. Click on the Restore tab in the DU main window.
4. Check the box labeled Erase destination.
5. Select the destination volume from the left side list and drag it to the Destination entry field.
6. Select the source volume from the left side list and drag it to the Source entry field.
7. Double-check you got it right, then click on the Restore button.

Destination means the external backup drive. Source means the internal startup drive.

C. Important: Please read before installing:

1. If you have a FireWire hard drive connected, disconnect it before installing the update unless you will boot from this drive and install the update on it. Reconnect it and turn it back on after installation is complete and you've restarted.
2. You may experience unexpected results if you have installed third-party system software modifications, or if you have modified the operating system through other means. (This does not apply to normal application software installation.)
3. The installation process should not be interrupted. If a power outage or other interruption occurs during installation, use the standalone installer (see below) from Apple Downloads to update. While the installation is in progress do not use the computer.

D. To upgrade:

Purchase the Snow Leopard Retail DVD.

Boot From The OS X Installer Disc:

1. Insert OS X Installer Disc into the optical drive.
2. Restart the computer.
3. Immediately after the chime press and hold down the "C" key.
4. Release the key when the spinning gear below the dark gray Apple logo appears.
5. Wait for installer to finish loading.

E. If updating:

1. Download and install update(s)
2. Use Software Update, or
3. Download standalone updater(s).

Youcan go for the far cheaper & newr OSX 10.6.x then...

Snow Leopard/10.6.x Requirements...

General requirements

* Mac computer with an Intel processor

* 1GB of memory (I say 4GB at least, more if you can afford it)

* 5GB of available disk space (I say 30GB at least)

* DVD drive for installation

* Some features require a compatible Internet service provider; fees may apply.

* Some features require Apple’s MobileMe service; fees and terms apply.

Which apps work with Mac OS X 10.6?...

http://snowleopard.wikidot.com/

It looks like they might still have it...

http://store.apple.com/us/product/MC573Z/A?fnode=MTY1NDAzOA

If it's a core Duo & not a Core2Duo, then it'll only run in 32 bit mode.

Might even be free I hear if you have a MobileMe account.