Disclaimer: I primarily host board/card game days with friends. Typically it is a very open-door policy with varying skilled players playing a variety of games, often multiple ones simultaneously. These guidelines may only apply to my particular set of friends and the types of games.
Something I think I do well is organize events.
I particularly enjoy hosting board and card game days.
Thanks to the stigma of playing games as being inherently nerdy/geeky be lifted and now that Americans are slowly getting a taste of delicious Euro Gaming instead of just playing Monopoly and Risk, maybe you want to host one as well.
I could talk about setting up your house, or how to invite people, or the careful management of food supplies, or making sure you can competently and patiently teach the games you want to play, or the secrets of how to manage the mix of players so that the good ones don't railroad the weaker ones. Nope, instead I'm just gonna blab on about the games I have and how to figure out which ones to play with your group.
The overall goal is to maximize the amount of fun for all parties involved. Sometimes this is easy. I know if I rounded up a few of my hardcore fellows we'd tear through Agricola or Twilight Imperium. Sometimes the crowd all wants to play together so you need something that facilitates large groups like The Resistance (and other Mafia variants) or Two Rooms and a Boom. But don't be afraid to suggest games they don't know. Because the real fun is when stories are told. For my hardcore players we dissect what could have been done better and the twists and turns of the mechanics. For my casual friends they like inside jokes about that one time in What-If we all picked on person X or when we played Fishbowl and this one action was for Ghengis Khan. So, finding the right mix in your game can make or break the evening.
Nothing worse than getting halfway through a game and someone storming
out because they're bored.
First, partition your group. If you have a lot of players, they will naturally need to divide up into groups to play different games. Luckily this often solves the problem for you. Hardcore gamers will be attracted to Agricola while the casual ones will want to play Dixit and Anomia. Giving a solid ten-second pitch of what the feel of the game is like is crucial here. Don't just talk mechanics, maybe touch on the theme, but get to what makes the game fun. Agricola isn't interesting as a farming simulator. It's fun because you're jockeying for resources and growing your farm and doing tradeoffs. Pandemic is fun because you are racing against the game as a team. Dixit is fun because you get to tell stories and look at cool cards. Red-and-Black is all about brinkmanship and bluffing.
If you need to suggest games for a group, assess their abilities and what they want to play. Some people will play anything and get a kick out of it. But some people only enjoy particular types of games. Here's a few classic example:
Casual Fun: One of my friends only wants to play games that "make you laugh." I originally thought this meant I had to find games where humor played a major role, like how Quelf makes you do stupidly random things or What-If's absurd juxtapositions about other people are good for a chuckle. But then I realized she also likes Dixit and Anomia. Why? It's not that she wants to just laugh, she wants a smooth game that doesn't require too much thinking. She wants stories to be created. Look for light mechanics or "everyone wins" sorts of games. Also, if there's a large component of randomness, it helps even the playing field when they go up against more veteran players.
Theme is King: One of my friends was on a zombie binge. World War Z, Zombie Survival Guide, everything zombies he wanted in. He didn't care about the mechanics that much, just if the theme included zombies. So Last Night on Earth would work perfectly! But, Betrayal at the House on the Hill could also work. Broaden the genre a little and see how beholden they are to theme. Be very careful with these players though. I once described Agricola as a "farming game" and another friend's eyes lit up. But I happen to know she isn't as interested in interlocking Euro-mechanics, she was only interested in the theme. A good theme can also help create fun situations. Mascarade [sic] involves switching roles, so it's quite fun to declare "I am the King!" or declare "I think you're the Fool!"
Skullduggery: It has been said that games can provide a great means of building trust with a person. You trust they played by the rules, you learn that they have honor, a quick mind, and perhaps a sense of humor. Then there's these guys. You suddenly realize they can lie to your face without blinking and you are none the wiser. They revel in Mafia style games like The Resistance. They gleefully sabotage the team in Shadows over Camelot. Any time they can inject a bit of in-game treachery they are there. Granted, much of this is derived from a sense of secrets and holding exclusive information. So hidden roles games (2 Rooms and a Bomb) or systems with traps (CCGs) can also sate their hunger. Much of the fun is due to asymmetrical information. So Shadow Hearts plays into this perfectly. Not only are there hidden roles and powers, but part of the game mechanics is to use cards to tease out information about the other players.
Roleplayer: It is super fun to take on a character and act out what they'd do. These players don't care that Flash moves far as a stat in Betrayal at the House on the Hill. They care that Flash RUNS REALLY FAST. Any sort of RPG elements can help. BANG! is a perfect hit, as is Cosmic Encounters or anything where you uniquely can screw with the ruleset. Note this also plays into persistence in other means, such as building how your faction plays in Risk Legacy. But this is also tightly tied to theme. 7 Wonders you're "building" a civilization, but not really embodying or roleplaying said civilization. Dominion sorta works since you are "building" your kingdom and then use those cards later. However, Thunderstone does feel like you're building an adventuring party that goes out and slays monsters, and it's uniquely yours.
Puzzles: These are the ones who approach the game like a puzzle to be solved. Thus, they tend to enjoy more co-op oriented games with deep systems. But they also have to be transparent and solvable. Pandemic as an optimization puzzle or figuring out the nuanced timings in Agricola fit these players. These trend towards the Euro-style games. They tend to dislike dice.
Brinkmanship: A very close cousin to only caring about winning, these people like the stakes to matter. So you have the Poker players, the gamblers, or people who like to play at the edge of what is safe. Red-and-Black is a great bluffing and reading game where you have to just overreach what is safe to win. Persistent tangible rewards, like in Risk Legacy, also help.
Competitive: Really all they care about is winning. Games that involve direct conflict like Risk are good. But also there has to be enough skill involved that it feels like they can control their fate (i.e. a Risk variant like Risk 2210AD). You can tell who these players are when they lose and complain about some random element screwing them over (dice in Catan are permanently cursed I tell ya). So they will trend towards skill-based games with clean mechanics they can exploit. Euro-games are a plus. But they will shy away from complex games they don't have mastery in since it's less likely they will win.
I probably missed a few archetypes, but you get the idea. And obviously lots of these overlap. Theme players usually enjoy Roleplaying. Competitive players usually like Brinkmanship and Puzzles.
So go out and game!