How to allow remote access without granting administrator rights windows server 2003/2008 R2 as well

Step 1:
make a group in active directory, you can call it whatever you want but for appropriation i suggest you name it something to the effect of Remote Access.

Step 2:
Go to the server you want to access remotely and click Administrative Tools > Local Security Policy.

Step 3:
In the Local Security Policy window, left pane, click the down arrow next to local policies and click User Rights Assignment.
 
Step 4:
In the right pane click Allow log on through Remote Desktop Services and add the group you created in step 1. Any user placed in that group will have remote access to the server we just configured.