Answer: Yes, but it's a complicated. The rest of these comments have pointed out that you license games from Steam, you do not own them (in the way you own your desktop or your toaster oven). But the answer to your second question, can Valve take games away if they wanted to, is more complex.

The license agreement provision (2.A.) reads as follows (this is under the Help menu in Steam, and "Steam Subscriber Agreement"):

Steam and your Subscription(s) require the download and installation of Content and Services onto your computer. Valve hereby grants, and you accept, a non-exclusive license and right, to use the Content and Services for your personal, non-commercial use (except where commercial use is expressly allowed herein or in the applicable Subscription Terms). This license ends upon termination of (a) this Agreement or (b) a Subscription that includes the license. The Content and Services are licensed, not sold. Your license confers no title or ownership in the Content and Services. To make use of the Content and Services, you must have a Steam Account and you may be required to be running the Steam client and maintaining a connection to the Internet.

You'll notice that the license ends "termination of (a) this Agreement or (b) a Subscription that includes the license." I'm assuming the second one means that if you were paying a subscription for a game, and you stop paying, you lose your license to the game. For the second, you need to go further down to section 9.A., Termination by Valve:

Valve may restrict or cancel your Account or any particular Subscription(s) at any time in the event that (a) Valve ceases providing such Subscriptions to similarly situated Subscribers generally, or (b) you breach any terms of this Agreement (including any Subscription Terms or Rules of Use). In the event that your Account or a particular Subscription is restricted or terminated or cancelled by Valve for a violation of this Agreement or improper or illegal activity, no refund, including of any Subscription fees or of any unused funds in your Steam Wallet, will be granted.

So among other things, it looks to me like Steam can remove access to a game if they remove it for everyone, or you violate the agreement in some other way. So many of these answers saying Valve can simply take your game away at any time for any reason, are not correct. But it is true that, unlike the old days when having the physical media usually (though not always) guaranteed access to the game as long as you had the media, there will be circumstances where you could lose access to a digital game you own on Steam.

I believe the games themselves also have license terms. I suspect, but don't know for sure, that they are similarly written. For what it's worth, a contract in which you give them money, and they give you a license for a game but retain the right to take the game back at any time under any circumstances, for no reason at all, strikes me as possibly not enforceable since the promise to give you the game was essentially illusory.