with an emphasis on VLSI, but probably applicable to any other eng-sci field
If one hasn't been showered with job offers already, chances are high he has had to send that sacred job application at some point. Here's my list of six questions one should (must?) ask along with the necessary work-related topics when seeking for a new job.
Work and work environment — As an employee you'll most likely spend 9+ hours daily at the job and you must be happy with what you do. Make sure you go check out the working conditions before accepting an offer, even if the office turns out to be on the dark side of the moon – do that! You should never accept blind offers based solely on telephonic interviews, unless you are super desperate and have absolutely no other choice. Not knowing what to expect when on your first day at the job might leave you disappointed. Never judge your workplace by its name and/or reputation.
Meet coworkers — Another important reason why you should visit your prospective employer is to meet your coworkers. Make sure you meet every one aboard the team. Typically, good groups will set you up on private interviews with future colleagues, which is an excellent opportunity for you (and them) to see whether you'll like each other. Are they...eeergh... idiots, slackers? Yes? Run fast!
Design practices — The individual private meetings are an excellent opportunity for you to ask more about the actual job, as well as getting a glimpse of their design practices. Are they trying to save from licensing costs by torturing their engineers do pointless heroisms? Just so the corporate boss can show off and say he's a great manager who just saved the company three bucks on behalf of your nervous system. This is also the time for you to ask counter-questions so you can see whether you should run fast.
The future — The group's future directly impacts you so don't hold your breath. However, be cautious, as there's a chance you'll hear a ton of lies on how pink the situation at the company currently is, expansion, profit, growth... You might also get a counter-question about your future vision (or whatever). Be careful what you're answering as such questions might have nothing to do with your job, but your employer might be just fishing and checking out what's under your hood. Here's a classic (in case you're applying for a jr. position) – "In the future would you like to take the management path or would you rather stick to R&D?" Remember what you're applying for, if you're asked anything similar be sure it's a trap.
Know your value — It really depends on your skills as well as the country and company you are applying at. Pay-related discussions might mostly be a trap for young players, but generally speaking the VLSI industry is pretty uniform and honest. If you are applying in the US or country with capitalistic views there's a high chance you get an offer that barely reaches the industry's mean level of pay. Don't be shy asking for more, but be careful – know your value, you cannot really ask 20x more than what you're offered initially... well, except for some special cases...
Backgrounds — Do your homework. Check the background of the group you're applying to. Ask former employees, be a detective, stalker, or however you want to call it. Glassdoor is one starting point.
Make sure you explore your options thoroughly!