The best replacement for easyshare is canon powershot.

The best alternatives to easyshare are rated as following:
★★★★★  canon powershot
★★★★  nikon coolpix
★★★  sony cybershot
★  cybershot
★  coolpix
  photosmart
  pulse

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Speaking about easyshare, one probably shouldn't forget about kodak.

Other search terms related to easyshare and their ratings are:
★★★★★ kodak
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Google Trends

Scale is based on the average worldwide traffic of easyshare in all years. Click on graph for more.
easyshare
canon powershot
nikon coolpix