Gateway Games (1 to 1 1/2 hours playtime / Simple Rulesets)
Settlers of Catan (Mayfair)
Carcassone (Rio Grande)
Pandemic (Z-Man)
Ticket to Ride (Days of Wonder)
The Adventurers (AEG / Fantasy Flight)
Dominion (Rio Grande)
Robo Rally (Avalon Hill)
Dixit (Asmodee)
Dvonn (Rio Grande) - one of the best games ever made. Sadly, not many people know of it
Medium Weight Games (1 1/2 - 2 hours playtime / Intermediate Rulesets)
Power Grid (Rio Grande)
Puerto Rico (Rio Grande / Alea)
Tomb (AEG)
Thunderstone (AEG)
Elder Sign (Fantasy Flight)
Manoeuvre (GMT)
7 Wonders (Repos / Asmodee) - Quick game (45 minutes) but can be a bit daunting to learn
Stone Age (Rio Grande)
Hansa Teutonica (Z-Man)
Memoir 44 (Days of Wonder)
Acquire (Avalon Hill)
Ascending Empires (Z-Man)
Ankh Morpork (Mayfair Games) - Just released and awesome
Talisman (Black Industries / Fantasy Flight) - Good intro to adventure games take 3+ hours of playtime but easy ruleset
Heavy Games (2 - 3 hours playtime / Time to teach/learn 30 minutes)
Agricola (Z-Man)
Le Havre (Z-Man)
At the gates of Loyang (Z-Man)
Through the Ages (Rio Grande)
Troyes (Pearl)
Alien Frontiers (Wild Mojo)
Nightfall (AEG)
Tales of the Arabian Nights (Z-Man)
Large Format Games (3+ hours / Extremely complex Rulesets)
Disclaimer: DO NOT START WITH THESE GAMES
Battlestar Galactica (Fantasy Flight)
Descent: Journeys in the Dark (Fantasy Flight)
Arkham Horror (Fantasy Flight)
Twilight Struggle - Wargame (GMT)
Merchants & Marauders (Z-Man)
1830 / 18xx : (GMT or Mayfair)
My Top 5 Favorites
Le Havre (Z-Man)
Battlestar Galactica (Fantasy Flight)
1846 18xx Game
Agricola (Z-Man)
Dvonn (Rio Grande)
What did we do before the internet?
Catan is very good. Have had many arguments playing that over a few brews, mostly the women arguing actually.
Dominion:Intrigue is an extension to Dominion, so assuming they already have Dominion it'd be a safe bet/buy.
riograndegames.com/games.html?id=306