UNIX:
The best Quicktime viewer for Unix is probably xanim. If it isn't already installed on Your system You can download the source from the -Home page and build Your own xanim or download the compiled gzipped executable for HP-UX or Linux x86 if You are using one of those systems.
If You are using a 256 color display and have enough memory and time use xanim +bCdhm -Cn {FILE} for best quality. Leave out the b in the command line if You don't have enough memory and time.

Amiga:
Here You can use the Amiga port of xanim, You may also execute setenv X11/askmode="YES" and copy ENV:X11 all to ENVARC: after installing xanim to get a screenmode request each time before playing a anim via xanim. If You are using DOpus 4 You can easily install the xanimate button. All You need to do is extract xanim_from_DOpus.lha to T: then start Your ConfigOpus and insert the Button. After that You probably have to change the xanim path - ready.
A much better better way to play Quicktimes on Amiga is in my opinion to play them with QT. This is the command line I use to play Quicktimes: "qt [] HAM8 MODEID "0x91800" LOOP"

Macintosh: A Macintosh without the ability to play a ? Never heard of.

MS Windows: Just try this one.