I'm using Google Photos (formerly picasa), WITHOUT all the other Google Plus junk.
Google photos is a no-frills option, but if you don't mind your photo size being limited to around 800 X 600 pixels, you can select the "High Quality" option (when you setup your account) and you get unlimited free storage. Since I never upload images bigger than 800 X 600 anyway, this option works perfectly fine for me.
If you want your original photo size to be retained, select the "Original Size" option and you get 15 GB of free space and buy additional space if needed ($1.99/month for 100 GB).