The best replacement for flickr is picasa.

The best alternatives to flickr are rated as following:
★★★★★  picasa
★★★★  photobucket
★★★  smugmug
★★★  shutterfly
★★  zenfolio
★★  zooomr
★★  ipernity
★★  snapfish
★★  instagram
★  tumblr
★  dropbox
★  500px
★  google plus
  imgur
  picasaweb
  picasa web
  kodak
  pinterest
  deviantart
  google drive
  google+
  pbase
  facebook photos
  fotki
  mobileme
  panoramio
  smugmug reviews
  picassa
  photo bucket
  yahoo photo
  google photos
  picasso
  picasa better
  shutterfly better

Your alternative for flickr is not listed? Suggest!
Speaking about flickr, one probably shouldn't forget about yahoo account.

Other search terms related to flickr and their ratings are:
★★★★★ yahoo account
★★★ picasa
★★★ twitter
★★★ compfight
You have in mind a companion for flickr and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of flickr in all years. Click on graph for more.
flickr
picasa
photobucket