Basically, no. You could make an alternate GUI, but it would not replace Windows, just sit on top of it. In fact, I once worked on such a GUI, called HP NewWave. It came out in the days of Windows 3.11, and added substantially to the features that Windows made available. Alas, HP didn’t know what to do with it, and eventually Windows added most of the functionality.
Plenty of alternatives to Windows exist, of course. You’ll get many respondents here saying that Mac OS is an alternative, but it isn’t, really. Others have already responded with alternative shells, but by themselves they are not alternative Graphical User Interfaces (GUIs).
As you note, your question comes from reading about various Linux GUIs. These are not limited to Linux; they could run on any fairly standard UNIX distro. I’ve seen both Gnome and KDE (two popular Linux ones) also running on Solaris. I assume they could run on FreeBSD as well.
All the UNIX GUIs I know of are based on the X windowing architecture. The basic structure of a UNIX OS is[ol]
[li]At the bottom, the kernel, set up for a set of hardware.[/li][li]Next, and still part of the core OS, the various file systems, programs, and structures that make up a particular distro.[/li][li]Off to one side, various command-line shells.[/li][li]The X windowing architecture, consisting of programs and libraries. These implement basic graphics interactions with a display.[/li][li]The desktop environment, such as Gnome or KDE. These come with GUI programs, widgets, etc. that allow you to interact with the core OS and with your machine.[/li][li]Finally, 3rd-party application programs that have been written for one of the desktop environments.[/li][/ol]
Now of course Windows also has layers like this. The difference is that Windows everything below the final level. You can’t do anything except write programs that use the API that Windows provides, so you can produce your own GUI unless you want to put it on top of Windows itself, as I’ve said.
In comparison, Linux lets you dig all the way down. Some wild and crazy SW engineer may be out there right now writing an alternative to X, for all I know. You could certain write your own desktop environment on top of X, and then you’d have an alternative to KDE or Gnome. In fact, people have done this, I just don’t know what the names are. My excuse is that I’m a technical writer, not an engineer.
You could even run Linux without X, if you wanted to. It would be much harder to use this setup, since you could only have one program in the foreground at a time. You need X for windowing.