If you have a similar base system (or use a docker container) You can add some arguments to the yum command to either just download the rpms, or have it download them and not clean them up...
So, following Alex's advice above... with, for example, a centos6.6 docker image and using the --download-only flag..
Here is a gist of all of the commands I ran and their output..
At the end, I had the following rpm's cached..
You could also mount a volume when you run the docker container so they are saved to your local drive.
docker run -v /tmp/rpm:/var/cache/yum/x86_64/6/ -ti centos:6.6 /bin/bash
and following the same commands as I did above puts my rpm cache directory in /tmp/rpm. Note that you need to use an absolute path for your host machine's path in the volume argument, I just spent a half hour wondering where my files went when I did -v rpm:/var/cache/yum/x86_64/6/