Gwenview does the same king of thing on KDE based Linux desktops (I presume you can install it on others), you can view pictures and videos one after the other, a slideshow, the ability to do basic editing, cropping, redeyes, resizing, save as and a few other things…light and fast and covers about 90% of the things you do.

When I switched my folks to Linux a few years ago, I got them to use Digikam to upload all their pictures and short videos because you just had to turnon the digicam.
But Gwenview was the default program for pictures and my dad really hasnt found the need for Picasa on Linux. He has used prior to picasa on Win programs like ACDC (sp?) and Irfanview so Gwenview was really super easy to pick up when we booted up his Kubuntu 10 Linux for the first time (he was using chrome, FF, VLC, OO but also non-FLOSS like Skype, Opera and we offered him Picasa but he said hed prefer KDE’s native Gwenview)