I recommend using Mathematica. The student edition was around $130 the last time I checked, and it's well worth it (if you're not a student, the home edition runs around twice that). Formulas are easier to write than in LaTeX, and you have the option of saving as LaTeX, as well as HTML, postscript, plaintext, rich text, and a few other formats. You also have the option of easily being able to play around with the math and see how it works, which you usually can't do outside of math programs very easily.
Mathematica is designed for notes, and there are already many (Mathematica) notebooks out there that allow you to play around with the math, very easily. I also recommend using a paint program running alongside Mathematica, such as Windows Paint Shop or something similar. This allows you to quickly draw a complicated diagram with all kinds of options, such as colors and effects, that are usually hard to do on paper. You can quickly add in pictures into your Mathematica notes, and their are additional options allowing further manipulations of the pictures in Mathematica.
It's easy to quickly make copies of your notebooks and play around with specific things in each copy. It's generally how I take notes, ESPECIALLY IF I'M IN A HURRY.
If you're planning on sharing you notes, you may prefer to use LaTeX if you feel that you're comfortable with enough time to use it. Generally I convert my Mathematica notebooks in LaTeX and then PDF when I'm sharing something with someone that doesn't have Mathematica. This, however, is generally reserved for when I'm going to make an important presentation, and I have enough time to really make the notes look pretty. However, simply converting Mathematica notebooks into another format is usually good enough, or even preferred if the presentation doesn't have to be spectacular.
It's really an art, not a science. I can tell you what has worked for me:
- Use a legal pad with three-ring punches where the sheets rip off clean at the top. I prefer a white one. After class, tear all your notes out from that day and put a paper clip on them. Store them in a manila folder dedicated to that class at your house. Also in this folder should be graded homeworks and other class materials.
- When you write notes, put the date of the class at the top of the
first page of notes, so later when you've got a bunch of various days of notes, you can tell at a glance the chronology.
- Number each page of notes from that day in the
lower left-hand corner (so if they get mixed up, you can quickly get
them back in the right order). Start back over at page 1 with each new class. If you end up having to insert a page in the middle,
call that page "6b" or something, and change the previous one to
"6a", so you can tell there should be a page between 6a and 7.
If you're on page 3, say, and you want to refer to something on page
1, mark it with an equation number or a star or something and save
yourself time by abbreviating it: for instance, writing "then using
(1.5), we get that (1.1) becomes (1.3)" is a lot quicker than
writing out all those equations again.
Directly after each class, do the following:
--Go over the notes quickly and write on the top of the front page, by
the date, keywords representing the topics covered that day. For
instance, "Poisson's formula", or "Proof that $e^{i\pi}=-1$". This
way you'll be able to tell in which set of notes a topic is covered
when you're looking for it later.
-- Go over the notes and isolate the things that require follow-up work
for you, and put those in your to-do list (you should have one!) For
instance, "Understand second fundamental form". Then later, use your
resources to take care of these. Do not just stow the notes away
and promise yourself that you'll "go over them" later. Unless you
isolate specific things that you need to do, they will just pile up
and turn into lumps of stuff you haven't taken care of.
Remember that the art of organization is the art of being honest with yourself: what are you really going to go back and do? What parts of the notes are you really going to look over and use later? Are you writing notes with the goal of advancing your understanding, or just because you want to feel like you're doing something?
For general organization tips (and getting the most out of notes is largely about organization), I recommend reading Getting Things Done by Allen.
EDIT: After a number of years, I would now recommend something like Notability for capture, and Anki for retention. Above all, don't rely on your intuition for when good learning is happening. Read the evidence (e.g. the book "Make it Stick" or www.learningscientists.org). Notes are generally low-utility. (Though of course you do need notes to capture information.)
Best Answer
This site uses MathJax, which has pretty much become the web standard Latex tool, because it's so easy to use.
You can get a free account at the Tumblr blogging site, and link MathJax in to it.
AFAIK, you can't incorporate MathJax into freely-hosted Wordpress.com sites. You can incorporate it into Wordpress if it's self-hosted. There may be other free Wordpress hosting sites where you could do it.
And apparently you can incorporate Mathjax into Blogger.
You can also link Mathjax to your own installation of various content management systems: Movable Type, Joomla, Drupal, MediaWiki, TiddlyWiki, and Moodle.
And just in case this question does get closed, similar questions could be asked and answered over on the WebApps StackExchange.
Edit: so, if it's a wiki you want, search for "free mediawiki hosting" or "free tiddlywiki hosting", and then look for one which will allow MathJax too.