Hi We live in Southern California. A tree (that we didn't plant) started growing in our backyard (about 20-25 feet from the house). We just let it grow. Its a good size now and we aren't sure how big it would grow. We also wanted to confirm that it wouldn't cause any damage to the house/foundation. Could someone let us know what kind of tree it is? I've attached some pictures. Thanks for your help. - Ranga
Welcome Ranga. Looks like Populus tremula. Common name Aspen. http://en.wikipedia.org/wiki/Populus_tremula
Probably Populus fremontii, probably harmless at that distance. Aspen is colonial so unlikely and only sparsely naturalized in the Eastern US. http://en.wikipedia.org/wiki/Populus_fremontii
Unfortunately, poplars are among the highest risk trees for causing subsidence damage to buildings; damage has been recorded at up to 30 metres range from large poplars. A lot depends on the soil type; if you're on sandy soil, no problem, if on shrinkable clay, definitely think about removing the tree now, before it gets any larger. Get professional on-site advice from an ISA-registered arboricultural consultant.
One way to tell the difference between the two species mentioned is that the juvenile leaves on the tremula are nearly round rather than a nearly triangular shape. The leaf margins on the two species are quite similar. The photo you included does look more like the fremontii which indeed is a tree that can become quite large.