Rabbit, *points to tat*, guess.
As rabbit said, several companies will pay for you to get a masters. I know the Lockheed Martin has a program like this (I can fill in more details if you're interested), and I'm sure other big ones do as well: Google, Microsoft, etc. I know that some of the government agencies prefer that you work on your masters/PhD while you work for them. Are you interested in math? If you are, you should check out some of the internships that the agencies within the DoD offer.
The problem is, though, they expect you to finish it in a predetermined amount of time, and you're forced to take a min/max amount of credits each semester (they'll only pay for so much). When I was talking with a professor and mentioned this, she recommended against it. She said she knew people who were doing this while she was going to grad school and she said that it "really took away from their grad school experience." I like being immersed in my academics, and I'm sure that this would take away from that.
Have you done any internships? I really think this would help you make your decision. After doing one last summer and talking with the aforementioned professor, I'm pretty well sure that I'm just going to skip the whole job thing until I'm done with grad school.
Good luck on this. It's a hard decision.
I've done two separate 10-week REU (Research Experience for Undergraduates) programs the past two summers (one at Texas A&M and one at Notre Dame). And I'm currently doing a paid internship with my university's IT department developing a web-based risk management utility for them, as well as developed a web-based call logging system last semester for them (unpaid) but am now getting paid to maintain this semester. Albeit, my internship experience is nothing comparable to working with a real company in industry.
Graduate school and working does not work well with me. I'd prefer to focus on one at a time, so that I can give my 100% to one instead of trying to share it between the two. That, and I wouldn't think I'd get as much out of the experience like you said.
Are you going for a masters or PhD?
If it's a PhD, it's less likely that a company will pay for it, IMO.
If it's a masters, it's more likely, but the disadvantage is that I imagine they get to meddle in your academic experience and exert some control over it.
If you can afford it yourself, I think (or rather, speculate) that it's better to go to grad school independent of a company. I believe it would make for a better experience, allow more freedom in your choices, and give you more control over your education. When you think about it, when a company pays for grad school, they have to be working in their own self-interest, so they're basically making an investment in you, which is a kind of repulsive idea to me. I don't want my education to be treated as a capitalist investment 
(Some may say that when colleges admit you, they are doing the same thing, but really I think the situation is quite different -- they don't restrict your education past general requirements, or stipulate that you major in X, Y, or Z.)
Of course, I have no experience in applying to grad schools, so take this post with a grain of salt
I'm applying to PhD programs. Assuming I complete said PhD programs, I will have earned my masters after the first 2-3 years and then the remaining years will be done doing research, dissertation, etc. So I'd finish with both a masters and doctorate.
For me, I eventually would like to teach on the post-secondary level at a more teaching-oriented institution like my alma mater. But I'm also interested in R&D in industry. Doing research in academia isn't my style though.
Like Chavo suggested, it won't be horrible which ever path I take. But I'd like to get it right the first time.
But I guess what really is starting to make me question my previous inclination to graduate school is how all the other factors in my life will be affected by the decision I make. The bigger picture. Up to this point, my life decisions have been made based off the goal of being able to find and get a job so that I can provide for a family someday. When I graduate with my bachelor's I will have met this goal, and it's a matter of how much more money can I provide, which to me will lead me down a slippery slope if I put too much significance on this goal.
Eh. I'm keeping my options open and will be applying to both grad skools and jobs. But I will have to make a decision sooner or later.
