I'm looking for a software to write mathematical equations in, that isn't LaTeX. There's no need to be able to write print them or make images of them, it's mainly for my own personal use. If there's a tool where it's possible to evaluate them also that would be even sweeter.
Mathematica allows to write mathematical equations in a semi wysiwyg interface, and of course provides extensive mathematical solving capabilities. It also provides some compatibility with LaTeX. It's not free, but there is a reasonably priced version for noncommercial home use, and even cheaper student versions.
If you're willing to consider LaTeX, LyX provides a userfriendly interface for creating your documents. But IMHO, it's only a gateway to learn "proper" LaTeX syntax... sooner or later, you'll get fed up of using the mouse and will want to type equations much faster.
Maple? That will allow you to evaluate them. EDIT: Credit to Kena for mentioning Mathematica; probably your best shot, but I'm sure Maple will do it too from what I remember of it.
Matlab can do a lot of evaluation work of mathematical equations, although I don't know if it can really sub in for a proper symbolic mathematics package.
MS Word's Equation Editor? That will allow you to write them out, at least for your own use. (And of course you can print them.) But you won't be able to evaluate them.

+1 for Maple. I've never used Mathematica, but Maple has always sufficed for my (admittedly basic) needs. – bcat Oct 29 '09 at 20:47
Check Mathematica (www.wolfram.com). They have free versions to write/read technical documents (and you can export them to Latex).. namely, Mathematica Player
I use MathCad which have a very intuitive way to write. You have a document where you can write text AND equations etc. And it does solving too. It looks a little old but is a great tool. I have also heard very nice things about Maple which is a little more lightweight.
MathCad and Maple is properly easier to learn because of the interface than Mathmatica.
TeXmacs for WYSIWYG editing of equations, with LaTeX or image file output. It also interfaces with other software, like Maxima, to evaluate expressions.
OpenOffice comes with a simple equation editor that will let you represent pretty much any formula. The syntax is easy to learn and you can export them to PDF. You will not be able to evaluate them using OpenOffice Math but WolframAlpha does an excelent job at that.
latex
because you don't want LaTeX. Outstanding logic. – Mica Oct 30 '09 at 0:10