This concern may be unfounded, but I shy away from third-party Twitter applications that require my Twitter password. I do this out of worries that it increases the chance of somebody being able to hack into my Twitter account. If you think that doesn’t make sense, let me know in the comments section.

Given that concern, though, there are quite a few Twitter-related applications that let you do a lot with information that can be gotten without your Twitter password, and I thought I’d begin a “The Best…” of them here. I’m sure I’ve missed a lot, though, so feel free to suggestion additional ones.

You might also be interested in The Best Resources For Beginning To Learn What Twitter Is All About and The Best Twitterers For Sharing Resource Links.

Here are my choices for The Best Third-Party Twitter Apps That Don’t Require Your Password:

TweetStats will give you all sorts of neat info and graphs by just typing in your Twitter user name.

Snap Bird is a search engine for “tweets” on Twitter. I may be missing something, but outside of subscribing to your own Twitter feed in your RSS Readers, this appears to be a great way to search for your tweets. In addition, you can easily search anyone else’s tweets just by typing in their user name and your own search term. (and you can do this without having to register)

Twitter Grader determines how “influential” you are on Twitter.

The 5K Twitter Browser shows what appears to be a visualization of the people you most recently have chosen to follow, and then do the same for those people.

Tweeps Key will…well, it’s complicated. But it’s a cool visualization.

I’ve never really understood why some people are concerned if the people they are following in turn follow them back. I figure I’m following people because I want to, not because I want them to follow me. But, if that is a concern of yours, Friend or Follow will tell you the answer to these questions: “Who’s not following you back on Twitter? Who are you not following back? Who are your mutual friends?”

Who Should I Follow? will give you lots of recommendations.

Follow Cost will tell you how “annoying” you and others are on Twitter.

TwitFlink lets you search links that have been tweeted by any user.

Tweetdoc creates a document that brings together all the tweets from a particular event or search term.

twitFlink lists only links a particular user has tweeted.

Mention Map is an application for Twitter that lets you visualize the connections any Twitter user has. It shows them in a cool display.

After you type in a Twitter user’s name to Tweet About, it shows you a word cloud of their most common word use on Twitter. In addition, you can search for people based on words you are most interested in.

The Archivist will create an infographic-like visualization of your tweets.

Twitalyzer is a free web tool that supposedly measures your influence in social media and the influence of others in your “network.” It doesn’t require signing-in to Twitter, though if you register on the site it will provide even further analysis.

ReadEvery lets you see the last several tweets written by everyone you follow (or the tweets from anyone another person of your choices follows).

8 Fun Twitter Tools for Language Lovers is a very interesting and useful post from Mashable.

Twitter Fountain lets you type in a search word and display tweets in an engaging display. It offers a fair amount more than that, and you can read about its features at Jeff Thomas’ blog.

“Your Twitter Followers Mapped” is a super-easy way to have your Twitter followers shown in a Google Map.

Tweet When shows you the days and times when you get the most retweets.

All you have to do to get a ton of data on your use of Twitter is type your user name into Tweetmetrics, and you’re given data galore.

Type in a user name into Tweet Topic Explorer and you’ll get a multi-colored word cloud in “bubbles.”

Hastagify is a neat Twitter app that lets you visualize connections between hashtags, as well as seeing all the tweets connected to a particular hashtag.

Type in some words into Tweetolife and in return you’ll get a visualization comparing how men and women use them on Twitter.

Tweet Wally is a pretty neat search engine for Twitter. You can read more about it at Tech The Plunge.

With Twtrland, all you have to do is type in a Twitter username and you get back a pretty neat profile of the person, their tweets, how many times they’ve been retweeted, and a bunch of other info attractively displayed.

Type in any name or topic into 25 Trends and you’ll get a neat visualization with links to related tweets. It seems useful and accessible.

Twitter appears to now let users get analytics of their tweets and their followers. Log-on to Twitter’s analytics page and you can see various statistics, including the number of tweets and retweets each day and month, the number of followers and “unfollows” you’ve had during the last month, and the gender of your followers. You can read more about it at this Slate article, Now Twitter Lets You See Which of Your Tweets People Are Actually Clicking.

Make A Cool Animation Of Your Twitter Activity

Again, I’m sure I’m just scratching the surface with this list. Additional suggestions are welcome.

If you found this post useful, you might want to look at the 470 other “The Best…” lists and consider subscribing to this blog for free.