Xbox One Early Adopters Reporting Hardware Problems

Though there may be solutions for you.

Update 2: A Microsoft representative provided this additional follow-up statement to IGN:

"The issue is affecting a very small number of Xbox One customers. We’re working directly with those affected to get a replacement console to them as soon as possible through our advance exchange program. Rest assured, we are taking care of our customers."

Update: One of IGN's office machines suffers from the same disc drive problem many have reported. When a disc is inserted, the Xbox One makes a grinding noise, but the disc is unaffected. However, Xbox One won't read any game discs. "Sorry, we can't play the disc," a notification says. "Try an Xbox One game, a music CD, or a movie on Blu-ray or DVD."

"We know that with a hardware launch of this magnitude customers will have questions and we have many avenues for customers to get the answers they need and get back in the game as soon as possible," Microsoft told IGN. "Rest assured we plan to take care of our customers. Any customer who believes they are experiencing an issue with their Xbox One should reach out to us through Xbox Support."
Microsoft customer support suggested IGN return the faulty unit to Amazon, for quicker results than going through Microsoft -- Amazon will replace the unit, whereas Microsoft will repair it. Both are viable options for victims of malfunctioning hardware, however, and Microsoft's @XboxSupport Twitter team has been addressing concerns all day.
With today’s launch of Xbox One, some owners are discovering various problems with their next-gen console.
An IGN reader's system is in an endless cycle of crashing and rebooting. Another has issues with his headset outputting nothing but static. Others have seen the "E100" notification, indicating a total hardware failure caused by an update error. The Xbox One troubleshooting page notes that this error requires you submit your Xbox One for repair.
You can do so via the Xbox Online Service Center.

Other new Xbox One owners have reported numerous issues to the Xbox support message board, including concerning issues with disc drives, unusual sounds coming from the machine, more spontaneous system shutdowns, missing pixels, and blank or frozen screens. Others can't get their systems to start in the first place.
In the video below, you can see the Xbox One making a horrifying grinding noise as the owner inserts a disc.
Of course, these are anecdotal instances of hardware malfunction rather than a representation of a larger, Red Ring of Death-level problem. That said, we've contacted Microsoft about solutions to these problems and any others. In the meantime, the IGN Xbox One Problems wiki page may have explanations for problems you may encounter.
If you're having any problems of your own, be sure to share them in the comments below, or contact IGN directly.