My first priority for keeping games was to keep those that my group enjoys playing and plays with some frequency.
Those games include:
Axis and Allies
Formula De (incl. tracks 5/6, 9/10, 17/18)
Twilight Imperium (3rd Edition)
Settlers of Catan
Ticket to Ride: Marklin Edition
We played Circus Maximus the other day (12.11) for the first time in years and introduced our children to this very fun game. They loved it. So much so that we are planning a cyberboard race in the coming weeks and months. I'm looking forward to that. It's always been a favorite of mine and one you can't take too seriously or personally (although we've had gaming vendettas bleed over from other games). You need to lighten up to have fun.
We had a group of seven and I ran two chariots, which in hindsight wasn't very fair to the others. It was a classic Circus Maximus game with plenty of back-and-forth. We shortened the race to two laps and I think we may have lost only one car in the final turn. Other than that it was a race down to the finish between three chariots. I'm sure we'll play this game again real soon.
Axis and Allies is a good "we want to play a complex wargame but don't want to read or review any rules." It's been a while since we've played, but always a lot of fun.
Twilight Imperium and Napoleonic Wars are similar games, but more intense.
The last three games were saved because they have family-wide appeal.
Please note that I do not bother to update my general boardgames (Uno, etc) as many families own these games.
Roll well and live!