Is it important to send a thank you email or letter after a face-to-face or telephone interview ?

Four things I have always learned from the interview process.
1) Always Always ALWAYS send a thank you e-mail/letter
2) Feel free to ask if there are any concerns about your skillset in relation to the job at the interview
3) ASK for the job during the process
4) Follow up about 2 weeks after the interview if you have not heard anything. The best way I did it was asking if there were any other questions that they had for you. I landed my two full-time civilian jobs this way.

At the very least, I tend to send a "thank you card." To not do anything shows a lack of manners. That is my opinion.

It's in good taste. That's what they teach Marines at TRS, but I haven't sent one cause I've gotten the job offer at every interview I go to.

I see 100% positive commentary about follow-up letters. I'll provide some counterpoint.
The letter will typically reinforce something. Better hope it's positive. So you must be a good writer, not sound condescending, whining, etc.

Know if a letter can actually make a difference. For Fed jobs, it had better not as it isn't an item that goes into the merit system considerations. So be aware you are trying to influence things in a non prescribed way and that's like football. Three things can happen and two of them are bad. Some hiring managers see that as improperly trying to influence and ignorance of the system. They are a minority (anal) but you don't know which ones are. My track record with them puts me in the nice touch but mostly irrelevant category. BTW a significant percentage of Vet applicants are poor writers and just reinforced my non hiring decision.

In the commercial sector, most thank you letters don't highlight a follow on opportunity. Saying something positive about what you saw that wasn't related to the specific job you interviewed for demonstrates you were outward looking during your brief visit and gets the hiring manager to ponder other opportunities for you.

What you're trying to do is to encourage the hiring folk to keep you in mind for other stuff that's coming up or perhaps to share your availability in their networking circle. So if you never hear anything back, that's OK. You don't want to go into pester mode. Bad word gets around more readily than good word.

Maybe...maybe not...but it sure created a reminder for the employer that you are there still and that stands out even if it is subtle. Kinda like being a crowd where everyone is standing still and then some one waves their hand in the air and waves your direction...

In addition, if you don't get the job then you should call and ask to speak to the person who interviewed you. If you get them, ask them, "For my personal growth, would you tell me what I lacked? This will help direct me in improving myself for a similar position in the future."

After years of experience Recruiting Talent, I can assure you that most candidates do not send a follow up communication. Which reminds me of tips from the book "What They Don't Teach You at the Harvard Business School" which as I recall was written by Mark McCormick. More common sense than anything else If no one else is doing it, and you do what ever "it" is, you are likely to stand out.

In recruiting this assumes that you are qualified for the position and that you demonstrated those qualifications that make the hiring manager consider you as qualified. Often times one has to walk the hiring manager through ones qualifications and potential impact to the position. And yes, sending a grammatically incorrect note won't help. And spelling the hiring managers name correctly also helps. It is the little things that are often most important.

If you are serious about the position, it's a must. Only a few candidates will do this, which is an advantage to those that do. This alone will not win you the job, but if it's a tight decision you can sway the verdict your way with such a classy move. Why not make every effort to land the job you want.

Letter is a great follow up!

Yes, even if it has little bearing on whether you get hired or not. It could be the deciding factor if it came down between you and somebody else equally qualified, but they put more weight on qualifications and experience than a cheesy thank you letter. Hiring managers know that the 'thank you" letters are customary and probably stopped reading all of them by now. If you have what they want and you aced the interview, they probably aren't going to care about the customary letter. But you should do it any way because it is one of those unwritten rules.