Greasemonkey is a hugely popular addon for most mainstream browsers. To me, this is my second most used add-on (first being DownloadHelper).
A GreaseMonkey script could be anything from blocking ads, to adding several different things to google search or a bot which basically browses the Internet for you. Greasemonkey is most known for Firefox; however, it can also be available (or at least run the scripts listed in this) for other browsers.
All of the links will be to userscripts.org which in my opinion is the best site for scripts.
In this article I will pick 5 of the best and review/describe them in a concise way.
Go straight to the Quick Selection Guide
BrowserBot is amazing. It is a bot that performs web tasks based on rules you give to it. Meaning you program a bot to do certain things. For example, repeatedly check a webpage for some special content and have the browser notify you as soon as it detects that content.
However, BrowserBot can do a lot more than just check webpages. It's built around persistent memory so that it can "remember" where it left off in its script even when the URL is changed.
The downside to this is that it is very complicated. It took me a long while to learn how to use it. I have only very recently learned there is a good tutorial on its website: http://www.kylepaulsen.com/browserbot.html.
Hide Google Instant Preview - I detest google preview; as do many, many others. This script removes that whilst being incredibly simple to install.
I would recommend this to anyone and everyone. (Obviously if you like the google preview then this isn't for you.)
VideoEmbed - Since video sites such as YouTube don't offer much useful content beyond the actual video (that's right, I'm disparaging YouTube comments en masse), there's no point in going to YouTube to watch a video when you could embed it directly in the page you're looking at.
That's the idea behind Videoembed, a script that automatically embeds videos from sites like YouTube, Google Video, and Metacafe whenever a site links to a video without embedding it. Now instead of clicking through to YouTube, you can watch the video directly on the site that linked to it. This is a must for ease of access.
NoDelay - Anyone who has downloaded files from sharing services like RapidShare or Megaupload has run into download landing pages that require visitors to wait from 2 minutes to maybe even 15 minutes before they can download the file they came for. The NoDelay Greasemonkey script takes you straight to your download, with no unnecessary pauses required.
Profanity Filter - The webs openness and impression of anonymity have redefined freedom of speech, but one side effect is that profanity has become ubiquitous online. The Profanity Filter script censors all of that naughty Internet ***, replacing common expletives with three harmless asterisks. This scripts default list of filtered words is large, but you can easily add words that you object to or to remove words that you don't find offensive. So, if you never want to see the word "Facebook" again, you don't have to.
This is one of the best child friendly scripts any parent could ever find.
eBayMaps - This is a very 'nifty' script intended to locate an item by one click when browsing eBay. For example, if you're looking for a local car then no need to message the user asking their location, this will find it for you!
GreaseFire - This isn't a script however it helps you find scripts. Basically when you install it (Firefox only I think) it lights up whenever you are on a page where there are scripts which you could install. Then you click on the icon and it takes you to a new window which gives you a list of the scripts, with details and with one click of a button they are installed on your system and in affect on the page. There is a downside though as it apears to slow down your browser (or it seemed for me). This is because it has to search the Internet on every page to find scripts - sometimes there are thousands.
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Hide Google Preview
Greasemonkey scripts, best free scripts, best greasemonkey scripts