My host is a freshly installed Ubuntu 2013.04, wireless network access worked out-of-the-box so I don't have any strange network configuration.
In VirtualBox 4.2.10, with default (NAT) settings, I installed CentOS 6.4 minimal.
Immediately after install, the first thing I did was ping 173.194.38.98 (google) and I a told connect: Network is unreachable.
I tried running /etc/init.d/network start as root, no joy.
I downloaded a VM image and tried it: exact same problem.
When I installed Ubuntu and Windows VMs, they are able to access the Internet without any problem.
What's wrong with this one?
On the VM:

On the host (values never change, except byte counts):
eth0 Link encap:Ethernet HWaddr f0:de:f1:c0:ad:b3
UP BROADCAST MULTICAST MTU:1500 Metric:1
RX packets:0 errors:0 dropped:0 overruns:0 frame:0
TX packets:0 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:1000
RX bytes:0 (0.0 B) TX bytes:0 (0.0 B)
Interrupt:20 Memory:f3900000-f3920000
lo Link encap:Local Loopback
inet addr:127.0.0.1 Mask:255.0.0.0
inet6 addr: ::1/128 Scope:Host
UP LOOPBACK RUNNING MTU:65536 Metric:1
RX packets:32272 errors:0 dropped:0 overruns:0 frame:0
TX packets:32272 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:0
RX bytes:4263162 (4.2 MB) TX bytes:4263162 (4.2 MB)
wlan0 Link encap:Ethernet HWaddr 60:d8:19:c9:42:59
inet addr:192.168.0.67 Bcast:192.168.0.255 Mask:255.255.255.0
inet6 addr: fe80::62d8:19ff:fec9:4259/64 Scope:Link
UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
RX packets:1221151 errors:0 dropped:0 overruns:0 frame:0
TX packets:845193 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:1000
RX bytes:1438957835 (1.4 GB) TX bytes:133904229 (133.9 MB)
Note: Similar to this question but switching from NAT to Bridge is not a solution I find acceptable.