Like others on this post have stated, going the extra mile for your customers cannot be underscored enough. I was the first person in IT to be recognized by our CEO for going the extra mile. I was the first person in the organization to be mentioned by name in several consecutive monthly IT staff meetings for going the extra mile and our CIO read the email he received from the top administrator at the site I support to the whole team as an example. My manager and I can't round at my facility without being told every 5 feet by someone new how they appreciate everything I do and how IT has NEVER been this open and welcome to them. I've currently been reassigned to this facility because the person who replaced me, who is a good tech BTW, never made it a point to just talk to folks and administration was frustrated. If I see someone I've replaced a PC for or fixed a printing issue for I'll stop them in the hallway and ask them how they're doing and how their issue is and I never walk past someone without acknowledging them. Recently when a VERY influential person in our organization had a workstation issue my CIO requested me, by name, to my manager to work with this person because they knew the job would get done, it would get done right and I would be thorough and follow up.
Documentation is also huge. If you're working on a ticket that takes longer than one customer interaction to complete and you suddenly get hit by a bus (or go on vacation) your team has to pick up your work with no idea of what was done. When one of my coworkers went on a vacation for two weeks I was assigned to his site and I took over his tickets. I spent the better part of 4 days apologizing to customers due to tickets that were 3 months old with such great entries as "unit is broken, vendor needs to fix" with no indication of who the vendor was, had he contacted them, are they coming out, when are they coming out or even what the blasted issue was that they needed to come out to resolve.
Be descriptive in the tickets you create while on help desk. Coming from an organization with sites in several cities and multiple departments in each site documenting where the customer is physically is equally as important as a description of the problem and your troubleshooting steps. "The printer doesn't work" is not an example of good documentation. "Ms. Smith called and reported that the printer in XYZ department constantly jams in the same place during every print job. The model of the printer is ABC and the IP address of the printer is 123. I was able to walk Ms. Smith through power cycling the printer over the phone but that did not resolve the issue. Ms. Smith can be reached until 2pm and then you can speak with Mr. White. If no one is available the printer is in the back hallway next to the break room."
Take the time to go through tickets you sent to other teams and find out what they did to resolve the issue. Have the mindset of "What I know I know but what I don't know I want to know."
Build relationships. I was on the help desk for almost a year then promoted to a desktop support role. We have several thousand employees in our organization but only 3 help desk folks. When I would introduce myself to new people when I arrived at the desk 9 times out of 10 the person would say "Wait, Nick from the help desk? OMG we LOVE Nick!"
Build relationships. The biggest thing we do in IT, especially the customer facing positions like help desk and desktop support, is build relationships with your customers. Talk to them. Listen to them. When it is appropriate, joke with them. Every so often check in with them to make sure they're OK even if they haven't submitted a ticket and they will LOVE you forever.
Work on your certifications and moving up. I put this one last because in your position on help desk it is the least important thing you need to be doing. Now, keep in mind it is still important, but you need to master the above skills first. A lot of my issues with help desk when I started a long time ago was that sysadmins had either forgotten what it was like to be the front line or didn't care. In my current organization a lot of our software analysts came from other fields so they have, literally, NO idea what it is like to have a 40 minute password reset phone call with a customer because they can't understand the different in shift and caps lock. They have NEVER had someone cry on the phone with them when you resolve an issue they've been struggling with for months in a couple of minutes (it's happened multiple times for me).