Just because you are getting married doesn't mean that you have to grow up completely and act adult all of a sudden. It's still okay to play games (as long as they are wholesome). Don't let anyone tell you that you should have outgrown the need for games when you get married. For heaven's sake, marriage is a game of sorts. How you play it is important. You need to play fair - I think that's in the vows somewhere - maybe not in so many words.
One of the important things now though is that now that you are becoming a "couple," is that you need to be planning games that will involve the both of you. The video games need to be put away or at least out of sight until your spouse is out for the evening for a commitment and so it won't be competing with his/her time.
Especially when you first get married, you may not have a lot of money for entertaining yourselves or others, but if you invite another couple over for a potluck or inexpensive dinner like pizza or Chinese food, you can enjoy playing games together with them. If both couples like some of the same games and you enjoy each other's company, you can have a great evening playing interactive board games.
If you like mental stimulation, you can play word games like scrabble or strategy games like Risk, but if you just like to have a great time and laugh it up, there are always games like Cranium, Apples to Apples, Catch Phrase, Twister, Battle of the Sexes, and Hand and Foot, to name a few. Games are such a great medium for interaction for you as a couple as for you as a couple with other couple friends.
One of the greatest games that will probably be around for a long time that is fun to play as a couple with other couples is the "Newlywed Game." What an eye opener it can be to play that game as a couple. Just when you thought you knew your spouse well, you find out that you think as much alike as you thought you did. That is a game that can be quite revealing. That is one game that is always a blast to play with a bunch of couple in the audience. What's amazing is that when played with couples who have been married a long time, often they don't do any better than the newlyweds on some questions.
The most fun games of course as a newly wed are those played behind closed doors - usually referred to as "Sex Games." Usually anything goes here as long as it is enjoyed by both players. Have fun with this one. As you discover each other and what's fun, the rules may change along the way. One rule that should never change, however, is that the game must be fun for both participants.