I want to implement something here that would deal with all sorts of requests (tech support or business processes that we don't currently have a system for) and allow them to be filtered and assigned to particular users. I'm looking at 2 different products:

Zendesk
SysAID

They both look to do what I want and seem quite configurable, anyone got any views? This is primarily for intranet usage although some tasks might be assigned to users outside the organisation. 25 users at the moment, I think it'll be 30 before the end of next year

I'm interested in this as well actually, but I've never pulled the trigger. Well, to be fair, I did purchase a license for FogBugz a few years ago, but personally, I think it sucks and it's over-priced. I'm also specifically looking for something that's not SaaS (Software as a Service).

Commercial is fine, but it's got to be a more traditional software license where I buy and I install - without the FogBugz style limits on how many people can access the software. One of the crap aspects of FogBugz was that every account required you to pay more money - that means you couldn't realistically use it to let your community/customers access the site.

SysAID has a free version and I thought ZenDesk did too, but I can't find it right now.

So far, I'm most interested in RT (Request Tracker) which also happens to be free: http://www.bestpractical.com/rt/

We've started using http://www.spiceworks.com/
It's free (ad-supported)

I've heard very good things about Spiceworks as well. I've been looking at its documentation for a while now, and I've formed a good opinion. Still, I never really tried it, so this is all theory.

Unfortunately Spiceworks is Windows-specific, so while it might work for someone else, it won't be suitable for me.

I need something that's going to be installed on a web server, likely running some linux distro.

Is it? Since I need to install it on Windows Servers I did not look into other supported platforms and I may not recall correctly, but Spiceworks has its own internal webserver (optionally, so, you don't have to use IIS), and I am fairly sure it supports MySQL besides Microsoft SQL Server. I really thought it was multi-platform.
Again, I may recall wrongly.

The download is an exe, so I'm pretty confident it's Windows-only.

Yup, Windows only:

http://community.spiceworks.com/help/Spiceworks_Requirements

Do *not* use ManageEngine ServiceDesk Plus. I'd also be quite reticent to try any of their other product. SD+ is remarkably awful, especially in its email integration, but it's quite bad in pretty much every aspect I've found.

I've used RT before, and it's very configurable, but it was a nightmare to set up initially. That may have improved in the intervening years, but I doubt it, as it intentionally had no defaults.

You might also want to look at Wikipedia's Comparison of Issue Tracking Systems.

We use zendesk at work for internal tracking, and it works great for us. For end users, it's just a magic email address. Assuming your organization is functional, I can't recommend enough having one email address for any issue. Need something purchased? Is the toilette backed up? Need a network jack activated? Send an email and get back to work, don't try and figure out who's in the office that day, knows what you need and is available to help you.

The folks at BestPractical would, I am sure, be happy to help you set some defaults

I hear what you are saying. We set up RT in 2007 and it was a bit of work for sure. But it has been spinning like a top ever since so we are happy that we took the plunge. The University's central IT org uses it as well to great effect -- single point of contact, just email "help".

I would say that the setup has gotten somewhat easier, too. Better avenues to handle all of the install-time perl dependencies for example.

Totally best bang for buck.

We've been using Cerberus Helpdesk for quite a while at our office and it's met our needs well. You may want to take a look at it.

So end users don't actually log in to the zendesk app at all? That's attractive, but how do users keep abreast of unresolved issues/requests?

The person updating the ticket can check a box to have the update emailed to the requester. The requester can always reply to any of the emails, which updates the ticket and sends an email to the assignee.

I believe zendesk creates an account automatically for everyone who emails, but most people never know.

Didn't know that, will have a play