Your comments

Can you try a "tracepath" or use "mturoute" on Windows?

$ tracepath -n 79.161.150.134

The "no route to host" error you get when telnet tries IPv6 does not seem right. Could there be an IPv6 routring/host resolve issue? Could you try to temporary disable IPv6. If using Windows just uncheck IPv6 protocol for the network adaptor. Or start Chrome and temporary disable IPv6 there: Using about: config and set setting network.dns.disableIPv6 to true
This is from a machine outside of my network:

IPv6:
$ telnet tellmon.net 80
Trying 2a01:79d:3e86:5a18:5945:87fd:f332:83c...
Connected to tellmon.net

IPv4
$ telnet -4 tellmon.net 80
Trying 79.161.150.134...
Connected to 134.79-161-150.customer.lyse.net


Could any of you do a simple connectivity test on port 80?
If you have telnet installed you can do the following from a command prompt:

telnet tellmon.net 80

It will try to connect to port 80 (http) on tellmon, it would be good to know if it connects at all. If you do not have telnet installed download a tool called portping that I made here: https://www.dropbox.com/s/2tth5ig7oqg0iiw/PortPing.zip?dl=0

Unzip and run from command prompt (requires .Net runtime)

portping tellmon.net 80
Then the issue is to figure out what all these networks have in common. The ones Jos mentions all seems to be related to Universities or science. Where do you work Mats?
@Jos: What do you mean. Can't you access tellmon.net from within the networks of UiT, npolar, nilu and akvaplan?
Or can't you access those web sites neither from the same network you have issues with tellmon from?
No problem, if you want to continue to dig that is fine. It would be good to track down the issue. I'm just out of ideas. I've run all the tests I can think of and I've spent hours googling and going through settings. But if you have any ideas or settings I can try please let me know.
Ok. Your account and data has been deleted.
Unfortunately this bug was fixed about 6 months ago. Anyways I did check the sysctl net.inet.icmp.reply_from_interface setting and it was already 1.

Tellmon has over 1500 users, the other web sites running on the same server has even more users. I find it strange that an supposed MTU issue should prevent 3 users access. My feeling is that a much larger group should have issues. I've tested the site with all the tools and checks I can think of. And none are reporting any issues.

Tellmon is available via both IPv4 and IPv6 from over 50 different locations I've tested from.
You account and all logged data has been deleted.