It's complicated!
Part 1:
You can check here: http://www.adobe.com/products/flash/about/ to see which version you should install for your Mac and OS. Note that version 10,1,102,64 is the last version available to PPC Mac users*. The latest version,10.3.183.23 or later, is for Intel Macs only running Tiger or Leopard, as Adobe no longer support the PPC platform. Version 11.4.402.265 is for Snow Leopard onwards.
* Unhelpfully, if you want the last version for PPC Macs, you need to go here: http://kb2.adobe.com/cps/142/tn_14266.html and scroll down to 'Archived Versions/Older Archives'. Flash Player 10.1.102.64 is the one you download. More information here: http://kb2.adobe.com/cps/838/cpsid_83808.html
You should first uninstall any previous version of Flash Player, using the uninstaller from here (make sure you use the correct one!):
http://kb2.adobe.com/cps/909/cpsid_90906.html
and also that you follow the instructions closely, such as closing ALL applications first before installing. You must also carry out a permission repair after installing anything from Adobe.
(If you are running a PPC Mac with Flash Player 10.1.102.64 and are having problems with watching videos on FaceBook or other sites, contributor Texas Mac Man suggests the following solution which fools the site into thinking that you are running the latest version:)
Download this http://www.steelbin.com/FPforFBPPC.zip to your desktop, unzip it, and replace the current Flash Player plug-in which is in your main/Library/Internet Plug-Ins folder, (not the user Library). Save the old one just in case this one doesn't work.
Part 2:
I am in the same boat. I cannot watch flash videos on the BBC website or on BBC iPlayer, although all other flash videos (YouTube for example) are fine.
For reasons that passeth all understanding, they work with the PPC version of Firefox, called TenFourFoxG5.app, once you have anabled plug-ins, as it does not natively support Flash.
You can download TenFourFoxG5 from here:
http://www.floodgap.com/software/tenfourfox/
Now for the interesting bit: TenFourFox, like Firefox, does not support most plug-ins. Unless you are prone to headaches (in which case don't) you can read about that here:
http://code.google.com/p/tenfourfox/wiki/PluginsNoLongerSupported
But there is a workaround!
Open TenFourFox and type in the address bar: about:config (no spaces) and click return. This gives you a warning that it might harm the application. Ignore that and click on 'I'll be careful, I promise' and you get the config file that you can edit - with great care.
Look/search (scroll down) for: tenfourfox.plugins.enabled
Set it to true. (Double click it to toggle it)
Now close TenFourFox, open it again, and Flash will now work, as it now uses the plug-ins that Safari has stored.
I am using Flash 10.1.102.64 in TenFourFox and it works just fine.