I must say, I'm bored of phpmyadmin. We are in 2009 and have to work with this usefull tool and to wait everypage to reload after every action. Are any ajaxed alternatives outhere? Maybe phpmyadmin himself is going to be ajaxized?
I found this one, though I haven't tried it yet: SQL Buddy.
PhpMyAdmin is working on an AJAXified version too, though it looks like progress is slow.
Try SQLyog. It offers much more than the PhpMyAdmin, but this is not a web-interface and its more like SQL Server Management Studio.
If you only care about providing yourself with an admin tool, not having web-access, and don't mind spending some money, I'd recommend Navicat for MySQL (http://navicat.com/en/products/navicat%5Fmysql/mysql%5Foverview.html). I love having one program to manage MySQL across multiple servers.
MonoQL is the answer. A modern AJAX client tool for phpMyAdmin. Check it out: http://demo.monoql.com. You can download it from sourceforge...
These aren't necessarily AJAX but thought I'd list them as they may be useful to other people:
I would recommend RazorSQL. Manage multiple servers, supports databases other than MySQL like PostgreSQL, MS SQL Server, SQLite, Oracle, etc. and has a PHP bridge if your MySQL instance doesn't allow remote access.
SQL Buddy might look cute, be fast and better than Phpmyadmin, but it has its limitations. It doesn't let you convert data upon insert, I mean say you want to enter data directly into the database like a user and the password field stores a SHA1 hash of the password, Phpmyadmin lets you convert your input to SHA1, MD5 and more, SQL Buddy doesn't. Small oversight, but it's something I find useful in a web SQL client.
Does it have to be web based? If you really want the responsiveness of a client app, you could use something like Sequel Pro (Mac).