We use ManageEngine Servicedesk here - the free version (I'd buy the pro version if I had the money). Been a happy user for many years at various schools.
I'm surprised that nobody has mentioned HESK Help Desk Software HESK - a free PHP help desk which is free, is pretty straightforward to set up and has a really good interface.
We have our own home built database but I've looked at alternatives from time to time, I couldn't get to grips with spiceworks - I just couldn't get it to work the way I wanted, I quite liked liberum but not enough to change what we've got. If money was no object I'd go for the netsupport helpdesk or possibly Richmond
+1 for Spiceworks. We have been using it for a year, and it's so effective. Highly HIGHLY recommmend it.
Which helpdesk does everyone recommend for students and teachers to be able to log issues?
Requirements are that it can auth using AD
Fits or ITIL
I will heartily recommend OP Smartdesk - only started using it recently in a test guise and we've been impressed by it's flexibility and moreso by the personal level of support provided by it's developer. There's an online demo to play with, free trial you can use and a free single technician version hosted by them if you so wish. Paid for version is pennies compared to most other solutions.
We're waiting for our budget to come through (hopefully soon, grumble) before we make a decision on whether we use the free version of pay for the full thing.
In my experience, having used 4 different help desk systems over the last 10 years, I have to say the modern variants are much better than the old, convoluted, and expensive systems that were popular at the turn of the century. Currently, I am a happy user of www.focalscope.com . It has all the features one expects from a help desk solution, but an interface that puts it together in a way that makes it easy to use, not confusing. That and the fact that it is reasonably priced + cloud hosted, made it an clear-cut winner for me.
Axios Assyst over here. Looks like I'm the only one using it too!