1. One of the biggest reasons why Americans have shied away from graduate programs in engineering is that we tend to be very uncomfortable with a degree that is so specialized. Most people who get a master's degree in engineering do so after getting an undergraduate degree in the same field, and having this combination of degrees requires a very narrow focus.
2. For all the concerns about job instability and outsourcing in engineering, a career in this field is generally far more lucrative at the lower levels than most others. Engineering is one of the few fields where average entry-level workers do very well right out of an undergraduate program. A lot of young American engineers don't go to graduate school simply because they are paid very well right out of school, and by the time they reach a point where their education presents a "glass ceiling" for them they are more interested in pursuing different career tracks within the field (a managerial track, for example -- which doesn't require an advanced engineering degree).
3. I would strongly urge any young engineer to steer clear of any full-time graduate program in engineering. If you want to get an advanced degree, do it at night on a part-time basis while you work a full-time job in the field. The experience you get on the job is worth far more than the education you get in the classroom, and delaying the start of your career by enrolling in a full-time graduate program could very well set you back several years.
4. Because of the universal nature of engineering principles, engineering has basically become "commoditized" to the same extent that manual labor has. From a purely technical standpoint an engineer in the U.S. is generally no more competent than an engineer in China or India, so for a truly rewarding career in engineering it is necessary to acquire skills above and beyond the normal technical skills in your field. This means expanding your horizons into areas at the periphery of engineering, or even completely outside it. A law degree makes an engineer ideal for a highly lucrative career in patent law, an MBA makes an engineer an ideal manager in a high-tech company, a combination of engineering and finance makes for a perfect Wall Street analyst, etc. Even an advanced degree in English can serve an engineer well, since people with good technical writing skills can command some extraordinary salaries.