TweetDeck's Web application, which made its Chrome Web Store debut back in December, has generally proved to be a worthy alternative to the TweetDeck AIR application for the desktop. However, up until today, the Web app only worked with Google's Chrome Web browser.  Now, says the company, TweetDeck is coming to all the major browsers, including Firefox, Safari, Internet Explorer and Opera.

According to a company blog post, the new beta of TweetDeck Web is a standalone website that requires no downloads or installations. Currently, it's working on Chrome, Firefox 3.6, Firefox 4 and Safari. Support for Internet Explorer 9 and Opera is arriving soon.

We covered the TweetDeck Chrome application back in December and found a number of things to love about it, including its support for HTML5 and drag-and-drop columns, its integrated inbox and replies section and its Foursquare column showing your friends' check-ins. Others clearly loved it, too - TweetDeck says the app is the most popular one in the Google Web Store.

However, we didn't have access to pop-up notifications, TweetDeck groups or streaming support at launch, which made it a little less useful than the desktop version at the time. Today's new cross-platform Web app still does not support streaming, the company notes. That means if you need speed, the desktop app is still your best bet.

For now, the beta is limited to a select number of users, but it will open up to more over time.

To get access, users can sign up to test the new site here: http://www.tweetdeck.com/webbeta. You'll need to specify what Web browser and version you currently use, so be armed with that information when applying.