As many as you can afford without unfairly taking time away from your family with a hard limit of 6 working and a project.
I personally like breadth and depth in a collection. I love modern Sterns. I love 90s DMDs, I love system 11s, I love early solid states... 6 is the most I can reliably keep going. I love trying out new machines and have found that temporary trades are the way to go to expand your collection and scratch that itch. If you have a Spike 2 Stern LCD game, there are 10-20 other games you can temporarily trade for if others with similar machines are around. We all like new stuff. One of my machines is a P3 with interchangeable modules, but I couldn't see keeping more than 3 or 4 because I just wouldn't have time for them. I can rotate the P3 module every week and have a different game every week of the month. Every other month if I get some mini games. I try and keep a couple of Sterns, one as a temp trade loaner (currently Bond) and one as a explore more deeply (currently Elvira). I have a favorite bolted to the floor game (STTNG... never see them in the wild and they are difficult to move), a Whirlwind, and an early Solid State (Xenon). I can temp trade those or sell/buy another game pretty easily. I'm debating the Whirlwind 2.0 kit down the road to be able to play 2 games on one machine. I'm hugely in favor of games that play multiple rulesets (see other threads). I'm scratching the tinkering itch with a Vulcan EM this summer. If all goes well I can pick one up at the Allentown show, fix one up for next to nothing, then sell it at the York show for what I have in it and have a different EM game to play every summer without sacrificing precious basement space. In other words, with 6 or so you can rotate them and keep things fresh.
Of course I'd be perfectly happy with just a World Cup Soccer (how I started off), or random system 11. I'm lucky and there is lots of location play around me. I try to avoid games I can play locally. I have expanded my arcade into a handful of Arcade 1ups (super easy to move) and some upgraded ones (I have a 60 in 1 and a Robotron home made). I just picked up one I'm going to convert into a knock off play choice 10 or just a Pandora's box. Arcade1ups are super easy to trade. I picked up a T2, traded it for an NBA Jam, and just traded that for a Killer Instict. I have a used coinop pool table that has been infinite fun as well.
I guess it really boils down to I've been having a blast with this hobby. I could replace my pool table/arcade 1ups with pins, but I'm trying to keep things "reasonable". Once you limit yourself on pins to a hard number instead of slowly adding as resources become available you cans start slowly upgrading. Thats essentially what happened once I ran out of space without being unfair to the family. Great discussion.