Today I'm going to go over several general mastery builds I use. I find masteries to be pretty straight forward, but I wanted to show people why I use certain mastery builds on certain champions. I also don't have the time to make a How I Play: Champion today so I'll do one tomorrow.
I have about 4 standard mastery builds and I'm going to talk about all of them and some small variations depending on the champion.
1. Standard Caster
This is the same build I use for Veigar. 9/0/21 works for most spellcasters, moving a couple points around in mid-utility depending on who you're playing. The biggest choice in this set-up is the 2 points in neutral buff duration which can be dropped into the % mana mastery if you feel you would rather have mana then a longer blue buff. I also tend to take ignite / flash so I get improved Flash. You can take improved exhaust over the crit point if you feel like using exhaust. Ghost can also be used instead of Flash.
2. Standard physical carry
This build is generally used for carries like Sivir who, while being primarily physical damage, do have a lot of magic damage. The points can be shuffled around the offensive tree and you can take more points in attack damage if your champion has an AD scale factor.
3. Physical carry w/o magic
When the carry you're playing doesn't have any magical abilities, or very few, like Ashe, I'd suggest something more on the lines of this. I prefer to take the defensive masteries because the armor / MR help early game laning a lot. If you want though you can take the utility masteries shown in the previous page.
4. Standard tank
I don't tank a lot, but when I do, I prefer to play Galio and such, so I take utility. However if you're playing someone like Rammus, going into offense could be very beneficial.
These are the masteries I use. You may use different ones and that's fine, there are many different ways to play the same champion. Play the game however you can be successful.