apache not accepting incoming connections from outside of localhost

In case not solved yet. Your iptables say:

state RELATED,ESTABLISHED

Which means that it lets pass only connections already established... that's established by you, not by remote machines. Then you can see exceptions to this in the next rules:

state NEW tcp dpt:ssh

Which counts only for ssh, so you should add a similar rule/line for http, which you can do like this:

state NEW tcp dpt:80

Which you can do like this:

sudo iptables -I INPUT 4 -p tcp -m state --state NEW -m tcp --dport 80 -j ACCEPT

(In this case I am choosing to add the new rule in the fourth line)

Remember that after editing the file you should save it like this:

sudo /etc/init.d/iptables save

CentOS 7 uses firewalld by default now. But all the answers focus on iptables. So I wanted to add an answer related to firewalld.

Since firewalld is a "wrapper" for iptables, using antonio-fornie's answer still seems to work but I was unable to "save" that new rule. So I wasn't able to connect to my apache server as soon as a restart of the firewall happened. Luckily it is actually much more straightforward to make an equivalent change with firewalld commands. First check if firewalld is running:

firewall-cmd --state

If it is running the response will simply be one line that says "running".

To allow http (port 80) connections temporarily on the public zone:

sudo firewall-cmd --zone=public --add-service=http

The above will not be "saved", next time the firewalld service is restarted it'll go back to default rules. You should use this temporary rule to test and make sure it solves your connection issue before moving on.

To permanently allow http connections on the public zone:

sudo firewall-cmd --zone=public --permanent --add-service=http

If you do the "permanent" command without doing the "temporary" command as well, you'll need to restart firewalld to get your new default rules (this might be different for non CentOS systems):

 sudo systemctl restart firewalld.service

If this hasn't solved your connection issues it may be because your interface isn't in the "public zone". The following link is a great resource for learning about firewalld. It goes over in detail how to check, assign, and configure zones: https://www.digitalocean.com/community/tutorials/how-to-set-up-a-firewall-using-firewalld-on-centos-7

SELinux prevents Apache (and therefore all Apache modules) from making remote connections by default.

# setsebool -P httpd_can_network_connect=1