There are only a few things you need for a huge game collection:
A job (nothing major)
A cheap source (flea markets, garage sales, pawn shops)
Luck
Time.
You won't have a 1,000 games overnight. It's taken me over 8 years to get where I'm at. I've pretty much just worked retail the entire time. I have a great source in a local shop that has plenty of games for less than a $1. I attend tons of sales and somethimes you just get lucky. Buying in lots is good too. Sell the doubles on E-bay, but stay away for buying. Shipping and other people get in the way!
As for time to play them (I don't rememeber who brought this up), not really. I've played everything I own, but only a few minutes max. There are plenty of games that get a standard rotation and popping in a truly awful game and sticking a friend with it is priceless. It's all the more for cataloging than playing. You just never know when a game will come up in a conversation. "hey, do you (game name)?" I'm always prepared!
Now, Portnoyd up there, his collection is awesome. His arcade room should be worshipped. It's gorgeous.