Used to use Altiris Help Desk (v6) before Symantec bought them and turned the product to crap (v7+). We wound up switching to Web Help Desk which was acquired by SolarWinds a couple of years ago. I like it for the most part, but dealing with support is a bit of a challenge.
Fairly light weight and runs on any platform with a MySQL backend. I believe you can get a free trial to kick the tires, or at least play with an online demo as both a tech and a user.
I use a combination of Trello boards and Git Issues. I rarely have long term support clients, though.
There seem to be some free ones out there that you can demo.
http://www.webhelpdesk.com/ Web Help Desk was purchased by Solarwinds and now integrates into all the relevant Solarwinds products.
Web Help Desk is incredibly great and you should buy it immediately.
WebHelpDesk is great. I can go on and on about it's features, but it's best you take a look at the site and see for yourself. They have a working demo on there for you to try out.
We use a barcode scanner, a bunch of cheap labels made by an online company (the vendor escapes me but I know there were several options) and a software called Webhelpdesk. In fact we move to webhelpdesk to do trouble tickets but it also has an extensive inventory management. Runs on linux (for now) windows and mac. Browser based and uses your choice of DB. The one user version is free, otherwise you pay by the number of Tech users. http://www.webhelpdesk.com/
WebHelpDesk has probably been the easiest out of box experience that I have had with a help desk. I have set up GLPI, OTRS, rt, HEAT and Track-IT!
WHD does a great job with inventory but does NOT do network asset discovery. It plugs in with several common asset software packages. I personally have it working with GLPI/OCS/FusionInventory at the moment.
GLPI is pretty powerful as a ticketing system also. It uses OCS/FusionInventory for asset discovery. Definitely not as sleek and sexy as WHD. It does, however, play with LAMP. WHD needs a Tomcat server.
Track-it had issues in older versions, but I hear its getting alot more powerful search features. However the price is not cheap.
If Keeping cost low is a priority try http://www.webhelpdesk.com/ as long as you have a server up the free iPhone app works fairly well.
We use WebHelpDesk. It does ticketing/client management/tech management/asset management. It even has some very nifty features (that we haven't implemented yet) like AD/LDAP sync which can pull location/user/and other data from AD objects. Great functionality for RDC as well as ARD and tons of other things.
I've used Numara Track-It, BMC Service Desk Express, and currently using WebHelpDesk.
Didn't really like Track-It, but it's been a few years. For me it was mostly an interface problem more than anything else. We were using the client version rather than a web version.
I liked Service Desk Express, but that may be overkill for what you need. I've only used it as a tech, not as an administrator.
I currently administer Web Help Desk where I work and really enjoy how it works. It's not by any means perfect, but in our organization it works pretty well. The best part is their support staff is very responsive. If you submit bug reports or request features, they'll usually respond back and fix it.
We've got multiple departments on it outside of IT using it. Users can submit their own tickets using their user credentials or via email. The system also can be configured so that you don't even interact with the web interface, you could have techs simply do ticketing via email. If you want, you can check out their online demo: http://www.webhelpdesk.com/demo.html