When playing D&D I keep about 99% core. There's too much total crapola out there for D&D for me to start letting books in ... much to the chagrin of one of my powergamer players. Not that he doesn't have enough to work with, as it is.
Heh. AND I seldom allow Monks in my games. Just an irrational prejudice of mine. Even though they're rather underpowered in core, from what I can see. I'm getting better about that ... really! It's always been a flavor thing for me.
Anyway, for D20 Modern ... I've never played it WITHOUT some sort of 3rd-party product. It's just something about Modern ... it doesn't demand support, but it's so easy to integrate things into it that usually I don't find a reason not to.
I'm the big Modern buff of my group, though, so I'm usually the person to bring things to the table, anyway. We also use a couple of house rules in D20 Modern which, for me, is extraordinarily rare. My usual opinion on houserules is "If I got paid to design it, and had the time to do so and playtest it, then I'd make rules too." Seeing as I've never been privy to the design meetings at WotC, I try to avoid it. Keeps me from buggering things up. But I did add a rule that individuals could use Auto and Burst weapons to get a +2 Circumstance bonus to attack rolls even if they don't have Burst Fire. That's about it. And some rules from Grim Tales.
I'm a bit of a control freak, though. If I don't have time to discuss and discard a couple character ideas with each of my players, and know my players very well on a personal level, I don't like them running their "own" characters. Even then, I usually prefer to collect character ideas and BUILD their characters for them. As far as I've seen it's never hurt the fun of the game, and has only helped, because I can hand-balance and make sure all of the characters are applicable to the game we're playing.
Every time I've let them stat up their own PCs I've regretted it later.
--fje