The best replacement for photobucket is flickr.

The best alternatives to photobucket are rated as following:
★★★★★  flickr
★★★★  shutterfly
★★★  picasa
★★★  tinypic
★★★  imageshack
★★★  smugmug
★  snapfish
★  imgur
★  instagram
★  flicker
  zenfolio
  flickr better
  picasa which is better
  picassa

Your alternative for photobucket is not listed? Suggest!
Speaking about photobucket, one probably shouldn't forget about funny gifs.

Other search terms related to photobucket and their ratings are:
★★★★★ funny gifs
★★★★★ meez
You have in mind a companion for photobucket and it is not yet here? Propose!



Google Trends

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