I forgot to add it grows from small rizomes. It comes up in small clumps for colorful leaves(for lack of better word).
Here is another pic of it.

http://img.photobucket.com/albums/v171/atokadawn/009.jpg

Looks like some form of Lirope to me. I could be wrong though.

Sometimes called monkey grass.

Can't really tell from the photos.

When it blooms on the "long stalk", is it a bunch of tiny blue flowers like tiny hyacinths, or is it a few larger blue flowers with three petals each?

It might possibly be a type of tradescantia (also called spiderwort). That's a very old passalong plant, and it has grassy leaves. Tradescantia makes flowers with three petals. Liriope makes the tiny blue flowers.

Here is a link that might be useful:

amazingdirt, that is it! Thank You oh so much. I have always loved these plants and carried some to each house we have owned. But never knew their name. They grow in the sun or shade.

Beat me to it. That Spiderwort will spread like wildfire.

Uh,... I mean it's REALLY great stuff!!! I'm bringing some to the MTPS.

Glad I could help. :-)

See I do not have a problem with it. I like to use it around the base of my trees and the walk.(so I do not have to weed wack)
But even the ones I have planted in flower beds have behaved for me.

There's a reason why passalong plants become passalongs. They are tough, attractive plants that don't mind reproducing themselves. :-)