On Ubuntu 14.04.3 LTS when attempting to run apt-get update, I get this:
Err http://us.archive.ubuntu.com trusty InRelease
Err http://us.archive.ubuntu.com trusty-updates InRelease
Err http://us.archive.ubuntu.com trusty-backports InRelease
Err http://us.archive.ubuntu.com trusty Release.gpg
Unable to connect to us.archive.ubuntu.com:http: [IP: 91.189.91.13 80]
Err http://us.archive.ubuntu.com trusty-updates Release.gpg
Unable to connect to us.archive.ubuntu.com:http: [IP: 91.189.91.13 80]
Err http://us.archive.ubuntu.com trusty-backports Release.gpg
Unable to connect to us.archive.ubuntu.com:http: [IP: 91.189.91.13 80]
Err http://security.ubuntu.com trusty-security InRelease
Err http://security.ubuntu.com trusty-security Release.gpg
Unable to connect to security.ubuntu.com:http: [IP: 91.189.92.201 80]
Reading package lists... Done
W: Failed to fetch http://us.archive.ubuntu.com/ubuntu/dists/trusty/InRelease
W: Failed to fetch http://us.archive.ubuntu.com/ubuntu/dists/trusty-updates/InRelease
W: Failed to fetch http://us.archive.ubuntu.com/ubuntu/dists/trusty-backports/InRelease
W: Failed to fetch http://security.ubuntu.com/ubuntu/dists/trusty-security/InRelease
W: Failed to fetch http://us.archive.ubuntu.com/ubuntu/dists/trusty/Release.gpg Unable to connect to us.archive.ubuntu.com:http: [IP: 91.189.91.13 80]
W: Failed to fetch http://us.archive.ubuntu.com/ubuntu/dists/trusty-updates/Release.gpg Unable to connect to us.archive.ubuntu.com:http: [IP: 91.189.91.13 80]
W: Failed to fetch http://us.archive.ubuntu.com/ubuntu/dists/trusty-backports/Release.gpg Unable to connect to us.archive.ubuntu.com:http: [IP: 91.189.91.13 80]
W: Failed to fetch http://security.ubuntu.com/ubuntu/dists/trusty-security/Release.gpg Unable to connect to security.ubuntu.com:http: [IP: 91.189.92.201 80]
W: Some index files failed to download. They have been ignored, or old ones used instead.
I've been able to successfully apt-get update and upgrade on this machine in the past. I'm not sure what changed. I can ping the addresses just fine. I'm using 8.8.8.8 and 8.8.4.4 for DNS. I'm not using a proxy.