From my experience, the best way to earn the respect of your customers/users is to consistently deliver good service. Do all the behind-the-scenes hard yards to ensure the systems you look after are stable, reliable, and performing well (even though the users never have any visibility of this, or appreciate just how much work it takes to do). When something does go wrong - when, not if - even if it is not your fault, be professional, polite, friendly, and above all keep the user(s) informed of progress (particularly if it takes a long time to solve the problem). If the users actually know you are working hard on solving their issues, they generally appreciate it even if they don't have a clue what you are actually doing.
Remember users are not IT people, and don't understand the complexities of IT systems. Even when a problem is entirely their fault (which is unfortunately frequent), try to explain to them in clear layman's terms the correct way to do whatever they are trying to do. Even if it is a case of colossal stupidity on their part, reserve your scorn and laughter for when you relay the story to your other IT colleagues, and not when talking to the user.
If all else fails, remember that being respected by everyone isn't a job necessity, nor is it always possible. It's very unlikely you will be able to please everyone all the time. In my job, I generally have a choice between having the users hate us (because we've allowed unstable/unreliable systems through to production), or having project managers hate us (because we won't allow their shoddy rushed garbage through in order to meet their poorly planned deadlines). I opt for the latter - my job is to provide services to the end users, not to make sure project managers get their bonuses.