First, do you mean update or do you mean upgrade?
Software update, upgrade--what's the difference? - http://support.apple.com/kb/HT1444
Updates you can do sequentially or use a combo updater.
Mac OS X 10.5.8 Combo Update - http://support.apple.com/downloads/Mac_OS_X_10_5_8_Combo_Update - extra note about repairing permissions after update: https://discussions.apple.com/message/9968141
If you mean upgrade, you can usually upgrade directly to whatever version you want, except in making the transition to 10.5 to OSX 10.7 or 10.8 you have to first install OSX 10.6 (as roam describes).
Start by checking if you can run Snow Leopard:
Requirements for OS X 10.6 'Snow Leopard'
Whilst Apple have withdrawn Snow Leopard from their stores, you can still get it from Apple by calling 1-800-MY-APPLE (if you are in the USA) and they will supply the SL DVD for $20 for a single user, or $30 for a family pack that covers up to 5 Macs. You can also purchase the code to use to download Lion from the same number (Lion requires an Intel-based Mac with a Core 2 Duo, i3, i5, i7 or Xeon processor and 2GB of RAM, running the latest version of Snow Leopard), or you can purchase Mountain Lion from the App Store - if you can run that:
If you are outside the US call your national Apple Helpline:
If you're in the UK, use this number: 0871 508 4400
When you have installed it, run Software Update to download and install the latest updates for Snow Leopard.
To use iCloud you have to upgrade all the way to Mountain Lion: