The first thing I used to say to a Twitter noob was: "Get a Twitter client like TweetDeck or Twhirl because using it on the web sucks".
After I discovered Troy's Twitter Script I have a different outlook on the Twitter web client. It simply does things that my Twhirl or TweetDeck client doesn't do. Here are a few features that I love (see install instructions at the bottom of the page):
1. Threaded Conversations
Ever wonder what those witty replies are referring to? Feel like you're missing half the conversation? Well, that's why threaded conversations rock. With this plug-in you see all of the backstory. Really, Twitter should have this. It's important.
2. Image/Video Preview
All of those TwitPics are instantly resolved and displayed in your browser. Awesome! Less clicking is cool!
Video too! It sure livens up a twitter stream when you start seeing photos and videos mixed in there.
3. Unrolling shortened URLs
Think of this feature like a preview of the pages that you might click on. It displays the page title much of the time and if it can't figure that out, then it displays the URL. Besides the obvious benefit, this is great for filtering out spammy followers and making sure you're going to a reputable site.
4. Easy Retweet Button
5. Who Follows You
A little smiley face shows up next to people that are following you. Good to know sometimes.
6. Profile Information on Followers Page / Groups
Profile info right in the followers area. That makes it easier to decide whether to follow back. Also, they have a group feature (like TweetDeck).
How to Install the Script
1. You have to have FireFox. Go get it.
2. Search for the GreaseMonkey add-in and install it.
3. Install Troy's Twitter Script.
Interested in what other sites you can hack with Greasemonkey?
Try adding Twitter Search to your Google Search: RealTimeGoogle script or Twitter Search Results on Google.
Still not satisfied? Check out ReadWriteWeb's Greasemonkey Scripts For the Social Media Addict. LOTS of great hacks, scripts, and mods in there.