As a guy who used to be on hiring committees, I'll share my experiences.
1. Always keep your resume fresh and updated on monster and/or similar sites. Don't worry about your boss or HR seeing your resume...it is your right to have your resume up and they probably won't care. Were I your manager and I saw your resume on monster, it would not bother me at all. If you are happy at "our" company then your happy...I don't have any real reason to worry that you'll leave. You do want to leave, I have two options. If you are replaceable I'll simply replace you when you leave. If I really need you on my staff I'll pay market demand to keep you / make you happy.
2. Always ask for more money when getting a new job...be polite and reasonable about it, but definitely ask. They expect it...they will be not be insulted by it. If that is best offer they'll make to you, they'll tell you that. Your workplace is not extended family (if it is, that is really sad). Business is business. Look out for you and yours.
3. In technical organizations (engineering, science and software) and probably in many other companies, as well, you future boss and/or his boss control the amount you get paid. If your future boss wants you he/she get can make a pay increase happen with a phone call...it is his/her budget after all, not HR's.
4. If asking for a little more money makes a company pull an offer...you probably don't want to work there because they obviously don't want you much.
5. If you are not currently employed then 2-4 may not apply to you. Companies do not like hiring unemployed people as there are always questions as to why you don't have a job. New college grads are generally excluded from this one but, still, beware...no matter how good your GPA is you are still largely untested in an employers eyes. you have to weigh your GPA, work experience, etc. and proceed carefully.
6. After being with a company for a couple years you should go on an occassional interview, just to see what is out there and make contacts, etc. Again, there is nothing wrong with it. Do not lead on a prospective employer...i.e. don't let them spend hundreds or thousands of dollars on the interview process only to tell then you are not interested. Your interviewing could influence your raises in the near future either positively or negatively. If you have a good relationship with your boss then you can use intel from your interview (or even job offers) to get nice raises.
I switched companies twice in my first 2 years because I was underpaid...that is not uncommon in the pharmaceutical industry, though. Then I stuck with one company until decided to go to grad school. Even so, I interviewed with other places three times and got two really nice offers. I didn't take them but I used them to show my boss my market value and it helped me get some great raises (my pay increased by 50% over 3 years).