Looks like Lily of the Valley - might as well be weeds, invasive enough.

I don't think they are Lily of the Valley.

Lily of the valley has multiple leaves off a tight single stem.

This plant sends up leaves individually from beneath the soil.

The midrib looks different too.

Consider this photo of lily of the valley:
{{gwi:305240}}

Is the mulch new? It looks like this plant arises from a straight root (or whatever).

Thanks for all the help and suggestions. Their leaves and stem look more succulent than those of Lily of the Valley. I don't use mulch in this area but compost instead. And I noticed yesterday that the same kind of plant also grows near my compost pile which is in a shady area so it looks like they can grow in both sunny and shady areas. Another thing is they all bunch up together. Maybe I will just let them grow for a while and see if they will reveal themselves. Or I can post a more up-to-date photo later on. Please let me know if you think of other possibilities. Thanks again everyone.

I'm thinking an aroid of some description.

I can't make out the veining, but it looks like some Zantedeschia, Calla.

Yes: they could be calla seedlings, or something similar. That would explain why they came up in close rows like that: they all grew from the seeds in one flower (and the ones by the compost were from a second flower). [I have some which are currently about 2-3" tall; one of the narrow pink callas planted by the Previous Owners.]

Do you have callas on the property, or something similar?

Here you can see photos of the fruit of a wild calla:
http://www.uwgb.edu/biodiversity/herbarium/Vascular_plants/calla_pal01.htm

I don't get to see many Zantedeschias but that is what it put me in mind of. I wasn't confident to go beyond aroid but you people are clearly familiar with them.

Amazing!! All of a sudden these all make sense now. I do have a single calla plant (Peace Lily) in the front yard and I remember several years ago I threw the foliage and flower stems into the compost pile in the fall. I just didn't realize callas can grow from seeds, let alone the seeds in the flowers can survive that many years in the compost pile!! I am so glad I did not kill these calla babies as weeds and thankful this forum has many knowledgeable people always willing to help out. Thanks a lot!

Hmm...Peace Lily (Spathiphyllum) is not the same thing as a Calla.

Yes, I got it mixed up. I have the calla with white flowers that look like peace lily but it should be a calla because it has a big tuber? Thanks for the correction. As you can tell, I know very little about these. At one time, I had pink and yellow callas too but they did not winter as well and all died... only the white one survived (and thrived). Thanks again.

Google Zantedeschia aethiopica and see if your 'Calla' with a white flower is that. Z aethiopica is a hardy plant. The brightly coloured, smaller Zantedeschias sold as pot plants in cooler climates are hybrids of other, tender Zantedeschias. The shoots you posted here look more like the tender ones to me - possibly the pink and yellow ones you thought had died?

I really wish these are yellow or pink callas too. They are so pretty.