Quicktime is Apple's venerable media player. It's always looked quite stylish compared to other well known media players, and at one time it was an obligatory download if you wanted to view. Mov movie files or embedded QuickTime panoramas, because Microsoft Media Player wouldn't touch them. Over the years it has developed into a more mature product which is able to play most if not all other media formats as well, and it should compete very positively with the free media player offered by Microsoft. There are plug-ins for all major browsers, allowing embedded QT movies and applets to be played anywhere. The controls have always been good and the app looks cool, as a lot of Apple products do. In addition the pro version has a number of cool features including the capability for live streaming over the web and conversion from one file type to another. The basic version is free.

So much for the good. The bad, is that QT has a reputation for being bloated even in its basic form, potentially slowing things down and wasting resources. By default it installs a tray icon which you won't need, and a small app runs in the background as soon as you start up, wasting more resources by checking for updates. And the updater is notoriously hard to remove, too. The free app keeps asking you if you'd like to upgrade. In other words, it's developed a reputation for being intrusive and irritating as well as being over-sized and resource-hungry.
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As a result, an independent application called Quicktime Alternative appeared some years back. It used parts of the original Apple app, stripping out the bits that most people didn't need, so that it was smaller and faster and still free. It went on to spawn QT Lite, smaller still. It's no longer being developed, though as ever, Google is your friend and in this case there is also a useful Wikipedia page devoted to it.

On the other hand, if you have a fast, modern multimedia PC running Windows and you want the full QT experience, which includes access to their QT site and things like movie trailers, go for the real deal. It handles everything up to H264 HD video and is going to be constantly updated to meet the latest developments, and if you have the resources it's still a very attractive player with excellent video quality.