One of the games that we recently played a lot is Splendor, a game with some really neat tokens, representing precious stones, and where the rich get richer (almost like in real life xD).
The objective of the game is to get 15 prestige points. You get prestige points from some cards and from visits from nobles. You buy cards with precious stones. But cards also represent mines, traders or jewelers, which give you more precious stones. So the more cards you have, the easier it is to buy other cards.
There are some constraints on how many precious stones you can have and how you can pick them up. In the beginning of the game, this can lead to a bit of a deadlock if everyone is hoarding resources, but towards the end of the game, most of the resources you need to buy cards will come from existing cards, so you will hardly pick up more tokens.
While it's a competitive game, there is not much in the way of player interaction. You only interact indirectly by taking cards that another player might also have wanted, but generally this isn't a big problem, because soon another good card will come for them. You do have to keep an eye on their resources and cards though, to make sure they are not trying to nab the same noble as your are.
The game is over when someone reaches 15 prestige points. Sometimes I wish the game lasted longer, because I was one step away from getting that expensive card, which would have then gotten me a visit from a noble and rocketed me to over 20 points. Oh well.
One last thing: I really like the holder that comes with the box. Everything fits in there really neatly and is easy to unpack and then pack back up.