You can get most Apps here without a Google account: http://en.uptodown.com/android If you go to their site you will see that each App has already been checked by perhaps 50 Anti Virus programmes to be safe – no doubt you can also run it past your own. This may be the next best thing to outright ‘jailbreaking’ your phone, which you might also consider if you are obsessed by privacy issues.
For example you can download the old version of ‘Pdf Maps’ which allows you to open an infinite number of maps. You have to uncheck ‘Update’ to continue its functionality. This is really good for opening GPS enabled Vicmaps on your mobile phone.