Have been using Flickr for a number of years and pleased with the service. You can set privacy down to individual pics. But you only have three options. Friends,Family,Public.

I tried Ovi a year or so ago, but could not move from Flickr because all my family are using Flickr as well. Tried using Picassa, but was not happy with the client integration on the PC where it really wants to be your photo manager as well and kept indexing everything on my hard drive. May have moved on in the last years though.

As usual YMMV. Register free accounts and try them all out.