Amazon provide VPN access with their Virtual Private Cloud (VPC)

AWS allow you to create your own private network 'in the cloud'. They call this VPC and it's fairly east to setup.

You can connect to your VPC in a number of ways, two examples:

VPN
You can connect to instances in your VPC via VPN (over an Internet Connection).

Direct Connect
You could also use Direct Connect to connect to instances in your VPC via a private network (ie NOT over the Internet).

Faster
Better ping/response times (more reliable)
More secure (as it bypasses any and all Internet traffic)
More costly (there are setup/ongoing charges with Direct Connect)

More Info

VPC & Peering
http://aws.amazon.com/vpc/

Also have a look at peering for communication between VPCs.

Connect privately to other VPCs- Peer VPCs together to share resources across multiple virtual networks owned by your or other AWS accounts.

Direct Connect
http://aws.amazon.com/directconnect/

Direct Connect & VPN
Setting Up AWS Direct Connect with VPN http://docs.aws.amazon.com/govcloud-us/latest/UserGuide/setting-up-direct-connect-with-vpn.html

Reference:

http://serverfault.com/questions/616805/join-ec2-instance-to-my-local-area-network