He instalado mongo en machine1 (Ubuntu 14.04.3 LTS server) en mi red local. También he abierto el puerto27017 como se menciona enesta guía utilizando los siguientes comandos:

sudo iptables -A INPUT -p tcp --destination-port 27017 -m state --state NEW,ESTABLISHED -j ACCEPT
sudo iptables -A OUTPUT  -p tcp --source-port 27017 -m state --state ESTABLISHED -j ACCEPT

Las reglas actuales son (iptables -L):

Chain INPUT (policy ACCEPT)
target     prot opt source               destination
ACCEPT     tcp  --  anywhere             anywhere             tcp dpt:27017 state NEW,ESTABLISHED

Chain FORWARD (policy ACCEPT)
target     prot opt source               destination

Chain OUTPUT (policy ACCEPT)
target     prot opt source               destination
ACCEPT     tcp  --  anywhere             anywhere             tcp spt:27017 state ESTABLISHED

Pero no puedo conectarme a este puerto desde machine2 (en la misma red):

$ mongo --host 192.168.0.108
MongoDB shell version: 3.0.4
connecting to: 192.168.0.108:27017/test
2016-01-23T18:02:14.848+0530 W NETWORK  Failed to connect to 192.168.0.108:27017, reason: errno:61 Connection refused
2016-01-23T18:02:14.850+0530 E QUERY    Error: couldn't connect to server 192.168.0.108:27017 (192.168.0.108), connection attempt failed
    at connect (src/mongo/shell/mongo.js:181:14)
    at (connect):1:6 at src/mongo/shell/mongo.js:181
exception: connect failed

También intenté verificar si el puerto está abierto o no:

$ nc -v 192.168.0.108 27017
nc: connectx to 192.168.0.108 port 27017 (tcp) failed: Connection refused

No estoy seguro de lo que me estoy perdiendo. Debe ser un error tonto ya que estoy configurando mongo por primera vez. Por favor ayuda.

Actualización (para las dudas planteadas en las respuestas actuales)

Sí, se está ejecutando. Puedo conectarme a mongo desde la misma máquina pero no desde la otra máquina. El demonio se está ejecutando:$ service mongod status mongod start/running, process 31205 y el puerto es 27017$ sudo netstat -tulpn |grep 27017 tcp 0 0 127.0.0.1:27017 0.0.0.0:* LISTEN 31205/mongodCambié elbind_ip a0.0.0.0 y reinició mongo. Sigue llegando el mismo error.

Troncos de mongo:

$ cat /var/log/mongodb/mongod.log
2016-01-23T16:28:13.155+0530 I CONTROL  [initandlisten] MongoDB starting : pid=31205 port=27017 dbpath=/var/lib/mongodb 64-bit host=dexter
2016-01-23T16:28:13.156+0530 I CONTROL  [initandlisten] db version v3.2.1
2016-01-23T16:28:13.156+0530 I CONTROL  [initandlisten] git version: a14d55980c2cdc565d4704a7e3ad37e4e535c1b2
2016-01-23T16:28:13.156+0530 I CONTROL  [initandlisten] OpenSSL version: OpenSSL 1.0.1f 6 Jan 2014
2016-01-23T16:28:13.156+0530 I CONTROL  [initandlisten] allocator: tcmalloc
2016-01-23T16:28:13.156+0530 I CONTROL  [initandlisten] modules: none
2016-01-23T16:28:13.156+0530 I CONTROL  [initandlisten] build environment:
2016-01-23T16:28:13.156+0530 I CONTROL  [initandlisten]     distmod: ubuntu1404
2016-01-23T16:28:13.156+0530 I CONTROL  [initandlisten]     distarch: x86_64
2016-01-23T16:28:13.156+0530 I CONTROL  [initandlisten]     target_arch: x86_64
2016-01-23T16:28:13.156+0530 I CONTROL  [initandlisten] options: { config: "/etc/mongod.conf", net: { bindIp: "127.0.0.1", port: 27017 }, storage: { dbPath: "/var/lib/mongodb", journal: { enabled: true } }, systemLog: { destination: "file", logAppend: true, path: "/var/log/mongodb/mongod.log" } }
2016-01-23T16:28:13.173+0530 I STORAGE  [initandlisten] wiredtiger_open config: create,cache_size=1G,session_max=20000,eviction=(threads_max=4),config_base=false,statistics=(fast),log=(enabled=true,archive=true,path=journal,compressor=snappy),file_manager=(close_idle_time=100000),checkpoint=(wait=60,log_size=2GB),statistics_log=(wait=0),
2016-01-23T16:28:14.444+0530 I CONTROL  [initandlisten]
2016-01-23T16:28:14.444+0530 I CONTROL  [initandlisten] ** WARNING: /sys/kernel/mm/transparent_hugepage/enabled is 'always'.
2016-01-23T16:28:14.444+0530 I CONTROL  [initandlisten] **        We suggest setting it to 'never'
2016-01-23T16:28:14.444+0530 I CONTROL  [initandlisten]
2016-01-23T16:28:14.444+0530 I CONTROL  [initandlisten] ** WARNING: /sys/kernel/mm/transparent_hugepage/defrag is 'always'.
2016-01-23T16:28:14.444+0530 I CONTROL  [initandlisten] **        We suggest setting it to 'never'
2016-01-23T16:28:14.444+0530 I CONTROL  [initandlisten]
2016-01-23T16:28:14.444+0530 I FTDC     [initandlisten] Initializing full-time diagnostic data capture with directory '/var/lib/mongodb/diagnostic.data'
2016-01-23T16:28:14.444+0530 I NETWORK  [HostnameCanonicalizationWorker] Starting hostname canonicalization worker
2016-01-23T16:28:14.949+0530 I NETWORK  [initandlisten] waiting for connections on port 27017
2016-01-23T16:38:37.046+0530 I NETWORK  [initandlisten] connection accepted from 127.0.0.1:37032 #1 (1 connection now open)
2016-01-23T16:39:31.447+0530 I NETWORK  [conn1] end connection 127.0.0.1:37032 (0 connections now open)
2016-01-23T16:49:24.240+0530 I NETWORK  [initandlisten] connection accepted from 127.0.0.1:37033 #2 (1 connection now open)
2016-01-23T16:49:38.249+0530 I NETWORK  [conn2] end connection 127.0.0.1:37033 (0 connections now open)
2016-01-23T16:51:51.707+0530 I NETWORK  [initandlisten] connection accepted from 127.0.0.1:37034 #3 (1 connection now open)
2016-01-23T16:51:55.785+0530 I NETWORK  [conn3] end connection 127.0.0.1:37034 (0 connections now open)
2016-01-23T17:32:15.546+0530 I NETWORK  [initandlisten] connection accepted from 127.0.0.1:37036 #4 (1 connection now open)
2016-01-23T17:32:21.180+0530 I NETWORK  [conn4] end connection 127.0.0.1:37036 (0 connections now open)
2016-01-23T18:11:57.885+0530 I NETWORK  [initandlisten] connection accepted from 127.0.0.1:37037 #5 (1 connection now open)
2016-01-23T18:29:55.365+0530 I NETWORK  [conn5] end connection 127.0.0.1:37037 (0 connections now open)