An Archive & Install should keep all your apps as you had them before the upgrade to Leopard. The Archive & Install, in a sense, bypasses the existing system, and installs a fresh set of system software. You will see when you choose that option, that you also have the choice to save your files and data - and you should make sure that sub-choice is selected.
You shouldn't lose any apps - although occasionally some will need to be reinstalled from your original disks. Those could be pro-level apps, such as Adobe PhotoShop, or maybe something like ProTools. Your experience may vary, but most apps will be no problem with an Archive & Install.
You may find some of your apps that need to be upgraded. You should check on all that you have for possible updates to support Leopard. And finally, some apps that you are using now may not work with Leopard. A common one is (again) Adobe Photoshop CS1, or older versions. The one prior to CS is PhotoShop 7 - which will not work - no fix to get it to work with Leopard.
So, there you are - it depends on what you have now.
Serendipity is a lucky guess !