My favourites:
Agricola - I think it's a brilliant game.
Variant on Settlers: place villages and roads with the resource tiles turned upside down, then flip them over. Place numbers on the board by picking out of a hat with various rules about where you can put them (no 6 and 8 next to each other, must place numbers next to your own villages first, etc.). If you've played 100's of times it's a way to shake things up.
Its hard for me to wrap my head around these two things being true at the same time. Settlers is so bad and Argicola so good. Settlers, for me at least, is hardly a game at all. Almost every action a person would take, such as building a road or building a dwelling, is clearly the best move. Anyone in the same position would do the same thing. Its just a matter of who gets the resources from the dice. A better game would be to roll dice a hundred times, each person choosing some numbers, and then find the winner. =) As you can see, I'm a big Settlers downer.
Recently played A LOT of Terra Mystica. Play online here against AI (probbaly should play a real game first, to know whats up)
http://lodev.org/tmai/
I like Euros plenty, such as Village, Power Grid, etc.
But there is "more" to a minatures games with battles, terrain, etc. I like one called Battles of Westeros. I use to dream about it!
Agricola is my S.O.'s favorite, but I have to be in the right mood or it just feels like doing chores, or even worse, stressful chores.
Dominion is my favorite; we have all the expansions, although I think Alchemy is a little weak.
Settlers of Catan is often our compromise game, but we never play the base version unless we are playing with little kids, teaching someone how to play, or using the expansion tiles to play with 6-7 people. We find it a lot more entertaining to play the Cities and Knights expansion with the Harbormaster and Fishermen thrown in to make it more strategic.
We both love Cosmic Encounter, Dungeon Petz, and Illuminati, but you really need more than two people to make these work.
When it is just the two of us and we want a quick game, we often play Jambo.
When there is serious drinking going on or younger players we usually go with Citadels, Muchkin, Carcassone, or Cards Against Humanity, depending on who is playing.
For us, what makes the difference in game quality is situational, not so absolute as your Agricola yes - Catan no.