We can understand something around 150 words, and even know how to intentionally deceive people and other dogs in order to get treats. We can be pretty sneaky! Dogs can even count up to 5 and tell you if a simple computation (like 1+1=3) is wrong. Dogs also have the capacity for spacial reasoning--like figuring out a faster way to get somewhere.
Intelligence varies by breed though. Border collies top the list for the smartest pups, with poodles coming in second. Read the article from Science Daily for list of the smartest breeds. Some dogs Coren calls "super dogs" that can learn up to 250 words. They rank among the top 20% on the bell curve, so I guess they should really be called "genius dogs." I think any dog with their own blog is probably up top!