Hah!
It’s also worth noting that if you are playing it as multiplayer solitaire, to some extent, you are doing it wrong, because you NEED to pay attention to what your opponents are doing, even if it doesn’t “directly” impact you.
Also, if you think it’s not “interactive” enough, try playing a game with the Witch,the Bureaucrat, and the Militia. 
For starter, Boardgamegeek.com is kind of intimidatingly big for a website, but the rankings are useful.
I play a LOT of boardgames; actually more than I want to (the group I’m in loves to try new stuff instead of playing the good stuff one more time). Like others, I will strongly recommend:
Puerto Rico – a wonderful game mechanic prevents the “nothing to do during other peoples’ turns” problem. There’s a reason this has consistently ranked 4th on Boardgamegeek’s list for years.
Dominion – at one point it unseated Puerto Rico, before slipping down a few ranks, perhaps due to overexposure – it’s wildly popular. If you use expansions, Dominion offers orders of magnitude more variety in game play than most others in this thread.
7 Wonders – a great game; although it has abstracted warfare in it, it doesn’t penalize the “loser” of these wars much, so it doesn’t breed as much unhappiness as some games. Helps to use a scoring app though, as scoring can be complex.
My newest hot discovery is Manhattan Project by Minion Games. Its looks are deceiving; 1940s style art and the dry topic may make it look dull. But it’s a “worker placement” game where the board is extremely fluid and there are a LOT of angles to consider and ways to interact. Halfway through my first game I made a note to buy a copy for myself.
Ra – the auction game that made me stop hating auction games. Well, okay, it’s the only one I like. Simple in appearance but fun.
I like Seasons too, but not as much as ones the above. It can be hard to find; I just special-ordered it and the expansions for my wife’s nephew recently.
Power Grid and Ticket to Ride are well-reviewed, but don’t quite float my boat. Lots of players love them though.
Munchkin is fun IF you understand its roots in D&D culture, but in our group, it has a reputation as the longest game anybody actually plays, and it does suffer from the “I’ll be on my smartphone until it’s my turn again” problem.
Regarding the Dominion nitpicking…a lot of the people I play with LIKE it being less interactive; they want to build their own little kingdom without interference. But there are a lot of attack and interaction-forcing cards in the expansions (most predictably, the Intrigue expansion is notorious for player-on-player attacks). More interactions might change your opinion.
Also, buying Silver and Gold and going directly for Provinces is called the “Big Money” strategy. It’s good…but there are lots of strategies that beat it (particularly “engines” relying on draw power and extra actions). In fact, the Dominion Strategy Wiki has a fairly technical article on Big Money that suggests that the test of a good strategy should be “does it beat Big Money?”
Regarding the “someone gets ahead early” issue, Dominion has a big balancing factor that slows the player(s) in the lead: scoring cards (Victory point cards like Provinces, Duchies, and Estates) do nothing for your hand. Buying a lot of them means drawing a lot of them – and doing it early means drawing them early – filling your hand with “dead” cards that weaken your turn. Is that mechanic not working well for you guys? It’s notorious around here.
Yeah, I think that’s a pretty good check on someone who starts buying a lot of Victory early; because in early turns you’re going to have a smaller deck as well so every Victory card comes into your hand that much more often. I had that problem when I tried playing a Chapel deck - I got a lot of provinces early, but then I had to sit back and try to buy more Gold while other players had a chance to make their moves (which involved playing a lot of Militias against me to further slow me down).
If it’s a family thing, you might like the “cooperative” game style as a change from competitive games. Pandemic is a good example of a “cooperative” game; it was my first experience with that type.
Another popular cooperative game among my set is Sentinels of the Multiverse. The players are superheroes facing a supervillain who is played by nobody (just a set of rules governing how he or she functions). The players cooperate to bring down the bad guy. The mechanics are not too complex, but the art and snappy quotes on the cards (from imaginary comic books those heroes supposedly star in) add a lot of character to the game.
I want to thank everyone again for the great suggestions above. I’ve ordered Dominion, and over the holiday weekend we found ourselves immersed in Timeline, a card-based game in which you draw 6-10 cards representing historical events, discoveries, works of literature, etc. Each card’s front and back are identical except that the reverse side contains the year the event/discovery/work was made. Each player, in turn, places his card in the proper sequence of the line of cards in the center of the table, and then flips it to discover if he was correct in the placement. Incorrect guesses must be replaced with new cards; the winner is the first person to get rid of all his cards. So the first one is typically easy: there’s one card in the center, maybe “The electric light bulb,” and it’s no trouble at all to play “The discovery of the wild turkey (by Europeans)” to the left of it. As the game goes on, though, it gets trickier – was the shopping cart invented before or after the stock market crash? My son thrives on trivia and history, and he has an excellent memory, so this is definitely in his wheelhouse, and between my wife, my son, and I, we each won about the same number of games. Some cards are gimmes (“The formation of the Earth,” was not a worrisome play) and some were daunting (Did the Iran hostages get taken before or after the invention of the compact disc?)
Inexpensive and great fun.
Thanks Bricker, that sounds like one my wife (the former history teacher) might even be willing to play. Let us know what you guys think of Dominion; my kids and I have been playing it a lot since I got it a few weeks ago (and we even went ahead and got one of the expansions this week).
Which one?
Dominion is a winner! Took a bit of careful re-reading to make sure we knew what we were doing, but a lot of fun.
We’ve just ordered Ticket to Ride: Europe and are trying to find a copy of Unspeakable Words, but it’s apparently sold out everywhere.
Yeah, I think it was a victim of a small print run and then being showcased on Tabletop.
My wife wants it and I can’t find it, either.
We got Dixit, and the timing was good – we were snowed in and all of us had an involuntary holiday from work and school. Really a fun game – quite a challenge to get inside each other’s heads.
Awesome! I’m glad you took me up on my suggestion.
Your tip was much appreciated!
For those that are wondering: the interesting dynamic with Dixit is the “getting in someone’s head.” The game rewards your ability to describe a artistic scene in a way that some, but not all, of the other players can pick it out of a lineup of other pictures. If no one correctly identifies your picture, you gain no points…but if everyone correctly identifies it, you also get no points.
Since my wife and son were the only other players, I had some interesting choices. A picture of a candle I played with the clue, “…and it seems to me that she lived her life…” My wife immediately picked up on the Elton John lyric; my son had no clue. And for a picture of a rabbit in armor I said, “It’s still a Normal/Ground type.” Bricker Jr. knew the only Normal/Ground type in Pokemon is a Diggersby, the evolution of Bunnelby, which is basically a rabbit. My wife doesn’t follow Pokemon to that degree and had no clue.
My wife said “Afghanistan warlord money,” and I correctly intuited that she meant a picture of a field of poppies.
Great game! (Even though I lost.) 
We also got Gloom!
The hilarious part of that game is tying the various misfortunes together into a semi-connected story. How, exactly, does someone who was just ruined by rum end up dying by being baked into a pie? According to my son, “He staggered to the bar’s bathroom and forgot which way he was going when he came out. Right next to the bar, there happened to be a commercial bakery, working overtime to make a giant pie for an upcoming wedding…and poor Darius Dark stumbled right into the mixer and was Baked Into a Pie.”
And on the next turn, he used the wedding against one of my characters, Lord Slogar, to make him Wonderously Wed.
And another update:
We played Takenoko this past weekend. What a great game!
I got Gloom and played it with my kids this weekend thanks to this thread. We only had time to play once, and the final score was 80-80-75.
My only complaint is that the writing on the cards is really, really small. But the transparent card dynamic is kind of different and we loved the pictures and text.
I actually started with the Intrigue set, and still found it fairly non-interactive. I can only imagine how lonesome the other ones are.
But I agree with you that I think a lot of people actually like that aspect (perhaps without realizing it). For awhile my group was playing Settlers of Catan quite often, and one of our friends would flip out and get really angry if anyone ever rolled a 7 and played the thief on her. She kept pushing people to place the Thief on non-inhabited regions or asked if we could even just play without it.
Also, I noticed that the OP mentioned Love Letter, and I forgot to comment on it. I picked it up a little while ago, along with another Seiji Kanai game, Chronicle, which is basically Hearts except each card played has a special ability, so there’s a bit more thought to it than “just play a card lower or higher than the current leader.” I’ve found that Love Letter is decent filler, but it’s a little too random and quick for my taste. I like Chronicle, though I also really like Hearts.
I played a game called Thurn and Taxis tonight which I really liked (maybe because I won). It has a mechanic similar to Ticket to Ride in that that there are six exposed cards to draw from on your turn, and you are trying to build routes that connect cities together for postal delivery - the board is a map of Bavaria and neighboring cities. But the strategy is much more layered than TTR. I can guess that some folks wouldn’t like it because of the limited opportunities to block the other players, but I thought it was a good strategy game and it was nice to have a theme that wasn’t medieval castles or zombies for a change :).
It’s been a while since we’ve played SoC, but when we do, we play with the paper clip variant. This means for each time a number is rolled and you don’t collect a resource, you collect a paper clip. For every 4 paper clips you have, you can trade those in for one resource. (A thief would take half the paperclips if you have over 7 resources). This helps keep the luck down a little bit more in the game.
There’s another variant she might like and that’s where the thief cannot be placed on someone until they have built/upgraded.
Otherwise, she probably just doesn’t like confrontational games.
Uh, did you PLAY with it, or just “possess” it? Because Dominion has the curious effect of not using most of its options in any given game.
Playing a Dominion game with lots of interaction cards there should be multiple “confrontations” of some sort every single turn once people actually like, have cards. Complaining about it before then is like asking why no pieces get taken in the first few turns of chess…