Can't Ping Ubuntu Guest from Windows 7 Host

NAT is the issue. Packets from the Ubuntu machine fly out of the machine, and onto the network. Router sees these, and sends them to your computer, because it knows where it is. then, VMWare ensures your VM gets the packets back, because that's its job. You get connection.

When pinging the guest, packets from the Windows host fly out onto the network and the router sees them. The router has no idea where your VM is, because VMWare has carved a tiny pocket out of your host for a private network. VMWare can't help the router find your VM, because at that point, it's outside of its sphere of influence. The router drops the packets, and moves on with life.

Here's VMWare's explanation of NAT configuration.

Put the VM on a bridged adapter. This allows your router to assign an IP address to it that it knows, and it sits on the network "next to" your computer. Then they can talk to each other.