I had shunned QuickTime way back when they started showing an annoying “Upgrade to Pro” nag screen when starting the application – what did it for me was that there was no “don’t remind me again” option. Instead I opted for QuickTime Alternative which was able to handle any .mov files I encountered. Both this and the excellent Real Alternative (I’m not a fan of RealPlayer either) are available here at the time of writing.
Anyway, it seems that you can get rid of the splash screen by setting your date forward a few years, launching QuickTime then clicking the “Later” button. Then set your date back to normal and you shouldn’t be reminded for those few years.
I’ve found that this works even if you have run QuickTime before (i.e. not from a clean installation). Strangely, QuickTime seems to crash on startup if you’re a little over-zealous with your date-setting: I tried both 2099 and 2050 with no joy, so settled for the more conservative 2010, by which time I expect I will have at least re-installed my OS and QuickTime.