Looks like baldcypress, Taxodium distichum. Got cones?

No this doesn't have any cones that I remember... at least I don't think. Would it have any right now? If so, it doesn't.

Metasequoia glyptostroboides -- Dawn Redwood

no, don't prune it! It's just a gawky teenager. Just let'r run -- she'll be magificient in a matter of a few years.

Haha, gawky teenager... yeah, I'll leave it alone then. I guess it's still fairly young then, I had no idea how long it was there. They must have planted it sometime before I moved in 3 years ago. Just googled it, didn't realize it was gonna get so big!

Yes, Dawn Redwood; the tree has opposite branching so it's a dawn Redwood. Baldcypress has alternate branching.
tl³

Thats an excellent tree with an interesting story. Nice close up on the leaves too.

Haven't seen any at the Big Box stores yet so someone at least put a little thought into plating it. You're lucky!

You can goodle 1010101 images of mature dawnredwoods and do a little reading about it's rediscovery. One of my favorites.

Here is a link that might be useful: Wikipedia Dawnredwood page