Hello,
I had this problem for a couple of days: I can't connect to my arch linux server machine (I know I shouldn't use Arch for this, but it's just a test). I started a TeamSpeak, Minecraft and Apache server, then I forwarded the right ports for them. I used noip to get a static ip address to my router, then I tried connecting via localhost (worked), via 192.168.1.41, my local IP (worked), via x.x.x.x, my router ip (worked) and with ****.ddns.net, the no-ip address (worked).
But if I try to connect to ****.ddns.net (or x.x.x.x) from another network, the connection is refused. By testing my open ports with the online tools it looks like the ports are closed. I tried disabling iptables:
but nothing changed. I don't really know what the problem may be. Obviously it can't be noip because nothing works also when connecting to my real (dynamic) ip.
Thanks for future answers.

Most ISP's block the ports for home users. They open all ports only for business grade connection.

But I had ports opened for years (not every port), and they have never been closed. Also, it doesn't refuse remote connections from local ips (e.g. I can connect from the server to the server using the remote IP), so I don't think the problem is that.

Have you ever be able to connect from a remote network?
Can you still connect from your LAN using your no-ip URL or router IP address?
Are you using a static IP or DHCP address reservation for your server on the LAN side?
It seems unlikely but could the ISPs be blocking the port?

I was able to connect about a week ago, but I don't think I changed something about the network on my system this week; I even don't think I updated the system (but I did that today, after the problem appeared);
I can connect from my lan using my no-ip URL or router IP address;
I am using a static local IP;
If the ISP is blocking the port, they are doing it manually, because I had some ports opened (and used) for years, with the same router and the same ISP.

EDIT: I just tried pinging the router from a remote network. The whole network can't be reached (doesn't say bad address, it just doesn't receive packets), so it isn't a ports problem.

By IP or URL?

Both.

If your router is configured to not respond to ICMP requests then the ping command will fail with x packets transmitted and none received with 100% packet loss. So that might not be a problem. If a remote port scan shows everything as closed then it could be an ISP problem. The router might be able to loopback so connecting from your local LAN may not mean much at the moment.

Is this really true?
I know some might block ports for web servers or mail servers to try and stop the spread of viruses and spam, but I thought most ISPs allowed all incoming traffic

I don't think it is an ISP problem. There was no problem some days ago. And in the webserver @ 192.168.1.1 (the router) I am able to set port forwarding...
I think it's a problem with my system. I will try as soon as I can to setup another server in the same network to test.

Does GNU/Linux have some configuration files for only accepting connections coming from the same ip?

EDIT: Yes, I just tried starting an apache2 webserver on an Ubuntu 14.04 on the same network, and I can connect from an external network, too (after setting port forwarding to it, static local IP etc). So the problem is my system.

Probably a silly question here - did you check for internet access on the arch server machine that is having the problem ?

I have a vague feeling its missing the default gateway or a route to the internet.

What does "route -n" on the arch machine show ?

Have you set up tcp_wrappers? Check if there is anything in these files: /etc/hosts.allow and /etc/hosts.deny.