

As Greasemonkey scripts are persistent, the changes made to the web pages are executed every time the page is opened, making them effectively permanent for the user running the script.
Greasemonkey allows you to write scripts that alter the web pages you visit. You can use it to make a website more readable or more usable. You can fix bugs that the site owner can't be bothered to fix themselves. You can alter pages so they work better with assistive technologies that speak to a web page aloud or convert it to Braille.
Let's say you want to make Gmail work better with filters & labels. To be specific, you really like folders and you wished that Gmail could work with folders instead. I'd head to Userscripts.org and search for "Gmail folders." The more you search, the more you'll see how things are listed. Side note: I personally made my gmail combine filter-use with labels and displays them as folders. It has truly changed how I use Gmail (see the screen shot on the side). If you like, I'd be more than happy to share with you how I've done that. Let me know in the comments, or shoot me an email to the ahmadism [squigly thing] gmail [dot] com
Some of you know me well enough to know that I'm a bookmarklet collecting fool. I don't want to spend too much time on what bookmarklets are, just know that they are JavaScript code that you run ad-hoc on whatever page you deem fit. To make them accessible to you, you put bookmarklets as links in your bookmarks/favorites. Usually right on your toolbar as shown in the image on the side. Whereas Greasemonkey scripts run on specified URLs, bookmarklets are on-demand. I use mine in place of extensions, especially toolbar extensions, whenever possible. This helps keep Firefox running smooth without any risk of bugs, viruses, etc. that come by way of extensions. Finally, bookmarklets run on Google Chrome (I'm a Firefox fan/user, personally) and on the iPhone (not an owner of one) without any glitches, apps, etc.
Never consider the possibility of failure. As long as you persist, you will be successful. - Brian Tracy
Your future is created by what you do today, not tomorrow. - Robert T. Kiyosaki
To succeed, you need to take that gut feeling in what you believe and act on it with all of your heart. - Christy Borgeld
The starting point of all achievement is desire. Keep this constantly in mind. Weak desires bring weak results, just as a small amount of fire makes a small amount of heat. - Napoleon Hill
You don’t have to get it right; you just have to get it going. - Mike Litman
It ain’t about how hard you hit, it’s about how hard you can get hit and keep moving forward. How much you can take and keep moving forward. That’s how winning is done! - Rocky Balboa
For every problem you ever come across, sit down and brainstorm 10 different solutions. - Brian Tracy
Positive thinking will let you do everything better than negative thinking will. - Zig Ziglar
I have not failed 10,000 times. I have successfully found 10,000 ways that will not work. - Thomas A. Edison
Keep the faith and just keep moving forward. Always remember, the more action you take, the more money you will make. The money will come, it’s almost impossible for it not to. You just have to keep working hard… - John Reese
The journey of a thousand miles must begin with a single step. - Chinese Proverb
Sometimes if you want to see a change for the better, you have to take things into your own hands. - Clint Eastwood
When you engage in systematic, purposeful action, using and stretching your abilities to the maximum, you cannot help but feel positive and confident about yourself. - Brian Tracy
I am not discouraged, because every wrong attempt discarded is another step forward. - Thomas A. Edison
Anyone who stops learning is old, whether at twenty or eighty. Anyone who keeps learning stays young. The greatest thing in life is to keep your mind young. - Henry Ford
The greatest amount of wasted time is the time not getting started. - Dawson Trotman
Perfection does not exist - you can always do better and you can always grow. - Les Brown
He that is good for making excuses is seldom good for anything else. - Benjamin Franklin
Better to do something imperfectly than to do nothing flawlessly. - Robert H. Schuller
Do, or do not. There is no ‘try’. - Yoda
Bonus Funny Quote:
Here’s something to think about: How come you never see a headline like ‘Psychic Wins Lottery’? - Jay Leno