Wine 1.6 is not latest version for Ubuntu 10.04, but you can install it by compiling the source code and it works perfectly. See demo here. To install Wine 1.6 follow the instructions.
Optional :
Wine Team recommend you to uninstall previous Wine versions when installing a compiled version. But its optional. If the Wine 1.6 fails you can uninstall 1.6 and use the old version.
Steps :
Download the Wine 1.6 Source Code from here. Extract the wine- 1.6 folder in the archive file to a place you desire. For Now, place it on your home directory.
The Wine-1.6 folder will look something like this:
Right click on blank space and click Open In Terminal.
Do the following command:
sudo make install
The program will automatically compile and install Wine. Also sometimes it might want some software to work and the software they want will be printed on terminal. Install it. If you need instructions Google It.
It might take up to 30 minutes to compile and install or maybe more. After installation the Wine Config window will look like below:
The styles of button are changed in the above window of Wine because I have installed a theme.