Garry's Mod ^[1]. The editing is far more complicated, but the social aspect is far less developed also. It's certainly not as casual as LittleBigPlanet.

Also, there is far more emphasis on the creating of vehicles etc. than of levels. But it's the closest you will get.

MineCraft ^[1] Is very casual. You build Pixel-art style buildings and levels out of blocks.

Atmosphir ^[1] has recently come out of beta, and it looks to be in many ways similar to LBP. It needs Unity, and its a browser game, but looks pretty full featured.

Create ^[1] from EA looks quite similar, but has not been released yet.

The Powder Game ^[1].

Technically it's a Java applet, not a PC game, but you can play it on the PC so I would say it qualifies.

The game itself is a physical simulation where you create particles from various materials, let them interact with each other (and with gravity) and also apply wind. Don't expect any fancy graphics, it's as basic as it can get - just colored pixels as particles and lines for air currents.

There's an impressive variety of materials, from stone and water, through gunpowder and rubber balls, to C4 that can explode and seeds that can grow trees if they have soil and water (and the trees create seeds of their own, and you can burn them, and fire creates upward air streams, etc. etc... you get the picture).

You can save your creation for everyone else to see, and there are weekly and monthly rankings. The game seems to be pretty active, and some of the creations are simply awesome.

A word of warning, though: the author's grasp of English is very poor, so don't rely on any decent instructions there. But it's easy to get the hang of things, and it's fun to experiment (e.g. will birds pop soap bubbles? And yes, there are bird particles and soap bubbles).

Kodu ^[1] It's available for the XBox and PC, and you can create your own levels and games.