Anti-aliasing (or AA) is a graphical enhancement which smoothes or softens the edges of objects. It can be said that it is used to remove aliasing or "jaggies". Many modern games have built in options to turn anti-aliasing on, improving the image quality at the expense of a slightly lower frame-rate. Minecraft, however, does not.
If you have a high end Nvidia graphics card, and are running Microsoft Windows, (I know it doesn't work on Linux, tell me if I'm wrong MacMen) you can do some magic to get anti-aliasing working in Minecraft, YIPPIE!
Here are some examples of what AA can do
Here's a link to the whole main screenshot. View fullscreen, and zoom in if you have a small screen.
Some of these images have been zoomed in to make it more clear whats going on. The texture pack is an old version of my own (link).
The effect here is obvious. The window frames look much better when smoother.
AA can reduce the appearance of wrong or badly-rendered pixels like the black spots in the torch.
Textures with lots of straight lines like my wood (lol?) are heavily ridden with "jaggies" without AA.
Strange patterns are often produced by aliasing (for example the planks here). Mip-mapping is a variant of AA that fixes this problem, but the full supersampling AA in the technique here also works.
The effect of AA is clearly seen when you have dark coloured blocks against light coloured ones (like the grass and sand in this picture)
How to force anti-aliasing in Minecraft
First off, you need a modern Nvidia graphics card and recent Nvidia drivers and control panel installed for this to work. Try right clicking your desktop, is there an "NVIDIA Control Panel" option? If not, you can't do this, sorry. Another check to do is that your getting at least 100 frames per second when running Minecraft. You can check this by pressing F3 in-game. Full blown 8xAA will most likely half your FPS, but you can always try to optimize if you need to (explained later). If you're playing on a laptop, unless it is a real beast, this is also not for you.
Below here are some recommended desktop graphics cards for using this feature. I have experience with playing with the settings on 4 different Nvidia graphics cards so I know what I'm talking about.
Run Minecraft (you don't even need to log in). Press Ctrl+Shift+Esc (or Ctrl+Alt+Del if you're still using Vista or XP) to run task manager, then open the processes tab. Find "javaw.exe" then right click it and select "Properties"
Highlight the location of javaw and Ctrl+C or right click -> copy to copy the text. Don't worry if yours isn't exactly the same as in the example.
Open the Nvidia control panel by right clicking on your desktop and selecting it or finding it in your Windows start menu. Click on the "Manage 3D settings option", as is selected in the picture. Press the "Add" button that is circled in the picture.
Click up in the location bar and paste (Ctrl+V or right click -> paste) the file location you copied earlier then press enter. Select (double click) javaw in that folder.
Change the options that are in bold in the picture to.. what they are in the picture. They will not be bold until you change them.
Make sure you "apply", then restart (or start) Minecraft. Oh look, even the yellow messages are anti-aliased and smooth!
After you've realised your FPS has taken a big hit (F3 to check); go back into the control panel and change the settings that are set to "8x", to 4x or 2x. You should keep playing until you find the combination you like that balances FPS and visual awesomeness.
I recommend 4xAA and 4xSS for a good balance. Having supersampling the same as or the level below the AA value is recommended, supersampling is the main cause of the FPS drop.
You MUST use 2x, 4x, or 8x Supersampling, NOT multisampling, otherwise you WILL get horrendous visual artifacts
More detailed information for cool people:
I hope you enjoyed and managed to follow the guide. If you can't get AA working by using this technique, why not bug Notch and Jeb like angry stalkers until they promise to implement AA into Minecraft fully.
If a lot of people have questions and/or get stuck, I'll make a short Q&A under here.
One more thing, thanks to whichever moderator moved the thread without complaining