What should I do? I would prefer more time to go through the interviews with other companies. In http://www.joelonsoftware.com/items/2008/11/26.html, Joel suggests to "accept the exploding offer at the last minute, but go to the other interviews anyway". Is this ethical? Is it reasonable?
As far as ethics are concerned, the company who issued the exploding offer is putting you in a bad spot and they know it. They're forfeiting their right to ethical treatment by not showing you the same.
There is NOTHING wrong with accepting the offer and continuing to interview for other positions. If you find something better just apologize and move on. It happens all the time and if somebody holds a grudge about it, they are being an asshole and you probably wouldn't want anything to do with them anyway. Seriously.
Moreover, it is important to keep in mind that big companies (and sometimes small ones) have no problem whatsoever with abruptly derailing the careers of good employees just for short-term financial considerations. Loyalty goes both ways and sadly big companies have burned that bridge first.
For example, in your case you should find out why they need an answer next week.
If they have a rule that offers can only be open for 7 days, you could ask them to issue the offer later after you've gone through your interview process.
Or if they have backup candidates they might need to engage, let them engage those guys, and you sync up again once your interviews are done.
And you should articulate your constraint: you have an interview "process" that continues for the next xx weeks, after which you can make a well-informed decision. You can also tell them it's in their interest for you to make a well-informed decision - they want someone who chose to work there for the right reasons and will be a long-term, productive employee. Turnover kills companies.
I wouldn't accept an offer unless you really intend to work there. One day you'll be a manager or director, and the karma will come back to bite you :) You always want to be a class act, even when confronted with someone less-than-classy.
If they're reasonable people and they want you, there's probably a good reason for their constraints, and they should be willing to find a solution that fits your constraints too.
If they're not reasonable people, or they don't want you, better to find out now.
Asking for more time only tells them that at this moment in time their offer doesn't interest you, and you'd like to shop around.
Every company believes they are the best place to work and what they offer is more desirable than other businesses and the ego of a large business is especially big, by asking for more time you might hurt their ego, they may only want people who desire to work for such a firm like themselves.
Do not ask for more time, interview as much as possible, and accept the job offer the day before or on the last day -- I think accepting the offer on the day before the last might convey that the clock didn't just run out for you.
If you get a much better offer later, take the new offer, it might not be the best move but this isn't so much a question of ethics so much as it's a question about burning bridges; nobody looks favourably on people who in hindsight only accepted because their ideal job wasn't yet available. These people will remember you and although they may understand the reason why you would do that, or they may do it or have done it themselves, it wont matter as you have wasted valuable time for everyone in the decision making and training processes.
Carefully choose whether you want to burn the bridge or not.
The other thing to do is check with your school's intern/co-op office and see if they have a minimum amount of time for a job offer. As I said before, my first job offer was 24 hours, but the school requires all employers operating through the school's listing service to give 2 weeks. If there's such a requirement you can use that as leverage to extend the date.
But never, ever, ever, ever give anything resembling loyalty to a big company. It is not a person, and cannot appreciate it, no matter how much you want it to. Until they're paying you, you are free to do as you please, ethically, legally and in every other sense of the word.
Assuming you accept, then stop going after other offers. You'll only upset yourself and/or burn bridges. Just chill out until you start.