What are the best Twitter apps or tools to improve the Twitter experience?

My Twitter presence would be nil without two tools:

Hootsuite ( http://www.hootsuite.com )
I run this 3rd party Twitter app through my web browser. It allows me to create different streams based on my Twitter lists. (If you don't use lists - you should look into them. They are a MUST for filtering your stream so you can be more strategic about your engagement.) Hootsuite also enables me to tweet from different accounts without having to log in and out of Twitter. There are a number of free (and pro) analytics and so forth. I haven't used these, but can see where they might add value. You can also use it's "schedule" feature to schedule posts in the future, but ...

That's what I use the Buffer App for ( http://www.bufferapp.com ). This app has changed the way I use Twitter. It has made it so easy and efficient for me to schedule tweets in bulk. By batching my tweet creation (the same way I batch much of my blog reading), I find I'm much more consistent with my tweeting. It's great to know that - whether I have time on a particular day to tweet manually, or not - my stream will be putting great content out for my network. Then, I can spend my "live" time on Twitter engaging in actual conversations and discovering new content that's not already on my radar.

I highly recommend both. Try them. It will change the way you tweet.
Good luck!