If you do not like desktop applications, you can have Twitter integrated into your Firefox browser with GreaseMonkey Scripts.

Greasemonkey user interface

GreaseMonkey is very cool Firefox extension!
There are hundreds of easy download able scripts available for Free.
Different GreaseMonkey scripts allows you to customize the way any web pages (eg.Twitter.com) look and with additional functions.

First install Greasemonkey Here, then install the scripts below.
All the scripts you install will be in your
Firefox > Tools > Manage user scripts (shown in the pic)
(*GreaseMonkey and some of the GreaseMonkey scripts are not very stable,
most of the time it works, but there are times when it is buggy and doesnt work.
Hope they will improve it further, because they are really useful & cool yeah!!)

Below are the coolest Grease monkey scripts that I recommend for Twitter:

Endless Tweets
Loads older tweets endlessly when you’re scrolling on the Twitter timeline.

Selectable Twitter Refresh
Selectable no. of minutes to refresh your Twitter home on the sidebar.

Twitter DM helper
Allows you to send Direct Message to multiple users at one time on Twitter.

Twitter Search and Tools
Adds Search and Tools in the Twitter sidebar.

Twitter Display Popular Trends
Display popular Twitter Trends on your Twitter sidebar.

Nested Twitter Replies
Adds nested replies to every Twitter conversation thread.

Kwout
A brilliant way to quote your tweets, works for Jaiku and Tumblr too. Excellent way to share the quote on your blog or anywhere else. Example of a quote click here.

Twitter friend name helper
Show list of friend names when you type “@” or “D”, works like address book.

Twitter Retweet
Adds a retweet button to the end of each twitter entry.

What the Tweet?
First i thought it should be a lame tool… “what the tweet?”?? Out of curiosity i checked it out and hey! It’s so cute! This script shows a different mouseover color for each tweet for easy view and it highlight any Tweet with just a click (to bookmark your last viewed tweet).

TwitPic Previewer
Preview twitpics directly on your Twitter stream.

*Tips: Subscribe to my blog or Follow me @casseylim for my personal account or @twitwebtester on Twitter to get the latest tools update!

If you do not like desktop applications, you can have Twitter integrated into your Firefox browser.

Twitzer user interface

Twitzer allows you to tweet more than 140 characters.
Twitzer allows you to type what you want, summarize it and offer a link for your friends to click on so they can read the full text version.

Personally, I would not recomment updates more than 140 characters, because the whole point of Twitter is to keep everything Short & Easy to read for busy twitpeeps.
So only use it when you really have to.

*Tips: Subscribe to my blog or Follow me @casseylim for my personal account or @twitwebtester on Twitter to get the latest tools update!

If you do not like desktop applications, you can have Twitter integrated into your Firefox browser.

Twitkit user interface

TwitKit places a side bar onto your browser which can be opened or closed at your request. You can type your updates and submit through the window, as well as view all recent updates by your friends.

*Tips: Subscribe to my blog or Follow me @casseylim for my personal account or @twitwebtester on Twitter to get the latest tools update!

If you do not like desktop applications, you can have Twitter integrated into your Firefox browser.

TwitterBar user interface

TwitterBar allows you to tweet from your browser search bar,
but does not show the updates of your friends.

Good for quick tweeting when you only want to tweet but do not want to be distracted by reading tweets.

*Tips: Subscribe to my blog or Follow me @casseylim for my personal account or @twitwebtester on Twitter to get the latest tools update!

If you do not like desktop applications, you can have Twitter integrated into your Firefox browser.

TwitterFox user interface

TwitterFox allows you to update, reply and get your friends updates on your browser.

*Tips: Subscribe to my blog or Follow me @casseylim for my personal account or @twitwebtester on Twitter to get the latest tools update!