PNG has always been my favourite format, the whole of my website just about uses it as well (gifs and jpegs used for large images and photos, gifs for alpha and animation) an animated png would be interesting unfortunately the only type I know is the fireworks animated png.
With my mod for GAE, I had to use TGA at first which is ok but having the alpha in a separate channel was very annoying and also windows can't preview them, though there are ways to have tgas displayed in explorer.
Now that PNG is supported, all my new textures are PNG format, though buttons are still BMP as they don't need alpha and are quite small, however I may start using png for them too in my third faction. I like PNG for its good compression, it's alpha and the fact that it's lossless and it's widely supported which is a bonus.
I've worked with dds before and it's very annoying especially now that I can't get the dds tools to work in Photoshop CS5 and that it's not a very supported format when it comes to modding. Having dds being used by the engine at runtime or via mod packers or whatever is ok though, so long as I don't have to constantly use some weird tools to convert tga/png/bmp to dds every time I want to make a slight change. As a 'background mechanism' dds is fine especially if it reduces memory strains which are a big problem for my mod at the minute, though it's more the g3d model format than the 2d mipmaps 'overload' that's a problem now.