Bernardyjh,

Thanks for the response. I'm sorry, I took the picture when I was on a tour of the governor's mansion in Denver. The woman who worked there didn't know what it was, only that it was a succulent. It sits in a glass room, so it gets a lot of sun.

Thanks again!

I think it looks like an old plant. Some of my sedums that are PIG look like that, but I generally behead and let the stems sprout new. It looks interesting! Wish I could help with an ID.

The leaves remind me of echeveria coccinea although the leaves on the picture appear more oval shaped compared to a more angular shape like the coccinea. I have to agree with Bernard; the plant is etiolated. Unless the room is made entirely of glass with a view to the sky, it's not getting enough natural sunlight as can be attested by it being indoors. With that being said, some like the look of the etiolation depending on the plant so, it's a personal choice whether to cut it back or not.

By etiolation, are you referring to the viney look of it?

Plants etoliate when they don't light they need - they keep stretching after light, grow much longer than they would otherwise. The leaves will be spaced much farther apart than under proper lighting. There are many succulents that trail-vine-drape; many are excellent in hanging pots/baskets or as a ground cover.

Here is photo of Echeveria coccinea (found on net) Neil mentioned (I don't know what the plant in your photo is) - it is trailing, but not as much as one pictured: