Tweet Nest is a web app written in PHP that you can install on your own web server or shared hosting environment. It stores your Twitter activity so you can browse and search it. Viewing is a really pleasant experience, as your data is organised simply and easily. Each month is selectable in a hybrid navigation-plus-bar-chart panel. Want to see what it looks like? Check out a demo.
If you don't like the default look, Tweet Nest allows for customisation. You can change colours easily in the config file or edit the stylesheet for full control. Really, since this is open-source software, you can do whatever you want.
Tweet Nest requires PHP 5.2 or higher (or 5.1 with the PECL JSON module installed) and MySQL 4.1 or higher. It's available for free right now.