Can I order the apps alphabetically or group them into folders?
Or maybe there's a better way of managing with an ever increasing number of installed apps?
The app drawer already does this for you.
Long press on the home screen. Click folders. Click New folder. Click on the folder to open it. Click on the "Folder" at the top to rename it. Drag and drop apps into the folder from the app drawer to place them into the folder.
I can also recommend Apps Organizer.
Install AppZorter app.
This is for Froyo or newer devices with TouchWiz (Samsung devices only).