Oh you poor unfortunate sudoer... However, this can be fixed!
First off, you need to know whether your Pi uses armel or armhf this can be found with a quick google search with the model of your Pi. Example: Raspberry pi 2 armel or armhf
(Sorry, I don't know off the top of my head...)
To get the armel version of the file run:
wget http://ftp.us.debian.org/debian/pool/main/d/dpkg/dpkg_1.17.25_armel.deb
For the armhf:
wget http://ftp.us.debian.org/debian/pool/main/d/dpkg/dpkg_1.17.25_armhf.deb
Once it downloads use the command:
ar -x <package name>
This will extract a few files. The one you want is data.tar.gz
extract it by using:
tar xf data.tar.gz
You now have a usr/
and sbin/
directory. One last command:
sudo cp usr/bin/dpkg /usr/bin/dpkg
Notice the positioning of the "/" in the last part of that command
Now you should again have the dpkg package back and be able to install packages to your heart's content.
Hope this Helps!