Alien Worlds - Simple, easy to get the hang of within about a week. Free to play, no enormous spend in crypto and if you need Wax for CPU or RAM, just go to Alcor Exchange to get TLM swapped for WAX. I haven't spent anything on it but I have already gotten NFT's worth a bit of WAX.
Splinterlands - Think Voltron art style marrying Magic the Gathering. It's a card game and has a huge variety of NFT's you can get. The magical book I think it requires you to get is $10 in crypto and your first NFT's will be around $4 dollars each
Blockchain Cuties - BCC has really adorable creatures like foxes, dragons, cats and many more. You battle them to level up and collect items. I got a free NFT just signing up. Their site is somewhat buggy but Discord is your place to talk to devs, which I have done a few times. The developers are actively posting updates, but you can play right now. Promising!
Find Any Free Sign Ups on Developing NFT Games - Look for any new NFT / blockchain game in Google search or Dappradar. If it hasn't been released and there's a sign up or subscribe somewhere, fill it out without hesitation. There's a very good chance you'll get a free NFT when these games come out. I found more games like Alien Worlds that aren't out and I'm excited to see when and if they release their games. Steam is also a place to be on the look out for.
Axie Infinity - This is a cute creatures game where you do breeding projects. To get started in March 2021, you need to buy an Axie. However, prices are so high it's almost stupid. There are Axies that are up for sale for $180+ million dollars. Although I would love to try breeding some creatures and get some NFT's - I need to shell out close to $400 which I'm gonna pass on for now. These NFT's are valuable, whether there is a bubble to be burst here or not, and if you can get a free breeding pair, get them! There are also land sales a la Second Life.
Sports NFT Games - I've come across golf and other sports games that required buying or depositing a lot of Ethereum or other crypto. I've passed on them, even if they give you a trial of an NFT to play around with. Just not my cup of tea, but I hear sports NFT's are very popular.
Upland - Some people really enjoy property buying games. In Upland you can buy properties and earn from people visiting your properties. You can also sell what you buy from Upland to other users. It looks like Google Maps with a property buying sim laid over it. The reason I'm not into it is cause of the graphics but I'm sure if I had some crypto to buy several good properties I might be more engaged by it. Entry barrier for me, but maybe not for you.