There are lots and lots of Twitter applicationss out there, and more are being developed as we breathe. Some cost, some are free, some are intuitive, some are not, but playing around with these apps on different devices, I've come to realize that different apps are awesome on different devices. For instance, Twitterrific works on both the iPhone and the iPad but its interface is better for the iPad. Most apps offer the same functions and the experiential difference usually lies in the user interface itself. Here is a list of common devices and which Twitter app I've enjoyed using on them most.
Twitter on the PC
Using Twitter on the website itself, sorry guys, is pretty unintuitive. You're better off using ANY other application. The one I like best is Tweetdeck. It comes with columns for all tweets, mentions, recommended people to follow, and direct messages. These can be customized and deleted as per preference. You can make a column for your lists, search topic and trending topics. When uploading pictures and video, you can choose which clients to upload your media too (twitpic, yfrog etc) The annoying thing is that lately, it's been crashing more and more but the user interface on the desktop is the ideal way to use twitter.Tweetdeck is free to download from tweetdeck.com.
Twitter on the iPhone
Until a little while ago, both, the Twitter for iPhone app and the Twitterrific app were the way to go for accessing Twitter on the iPhone. However, the latest update of Echofon, in my opinion, has redeemed itself to become a pretty user friendly app given the interface and size limits on the phone. The feature I like best is when typing a mention, it automatically gives you options for the twitter handles of people that you follow and follow you. It's integrated lists in the app and is a lot less buggy than the other two. Pictures are automatically uploaded to twitpic. Echofon is available in the app store for free and there is a pro version as well for $4.99.
Twitter on the Blackberry
Twitterberry is the app of choice on the Blackberry. Twitterberry is free and and has a pretty simple user interface. Again, here you have a choice of whether you want to upload your pictures to twitpic, yfrog, twitgoo, etc. Here too, there is active text recognition for mentions and hashtags and you can perform twitter searches easily.