$1,000

[Jumpman Jr.]

The Master System would be the easiest, and closest to the $1000 mark. As was said before, the 7800 would follow.

Id also think that you could manage a complete 5200 collection, maybe Intellivision. (Im thinking how low the prices for intv stuff currently is)

R-Zone would be obtainable as well

Intellivision... eee. Maybe, but doubtful. I've got a complete Intellivision collection, and I'm pretty sure it cost me more than $1000, and I got some of the rarer games for really low prices. Especially considering how high Spiker! and the other later-releases have been going lately.
As many other people said, Master system is doable. But it would be tough. I've got a complete SMS collection, I probably spent about a grand on the whole thing.
N64? Bleh, Maybe, but only if you get a LOT of the games at some big sale where they are selling off ex-rentals for $1 a pop. What I've been finding is that a LOT of the non-sports N64 games, when boxed/complete, go for $10-$20, which is fairly high for an average price of a game. And there is like 300 games for the N64, so that would be tough. However, there aren't very many extremely expensive ones, just a few that are around $50. I still need about 50 N64 games to complete the library, and I'm pretty sure I've spent more than a grand.
Now, Dreamcast. That would be hard. However, I have a 100% CIB Dreamcast collection and it only cost me $1500 Canadian, which is about $1200 US. Possible, but hard.