Yes, there are many standard datasets but which medical images you mean?

There is standard Digital Image Database for lung nodule

http://www.jsrt.or.jp/jsrt-db/eng.php

Liver segmentations

https://www.virtualskeleton.ch/ShapeChallenge/Start2014

Also, brain tumor segmentation

https://www.smir.ch/BRATS/Start2015

If you are interested in one particular organ, I would suggest doing a search on challenges put forward by various conferences in medical image community.

Here is one place where you would have access to many challenges.

http://grand-challenge.org/All_Challenges/

Yet, the list isn't exhaustive.

You will probably come across the new trends when you go through the different approaches of different contestants.

The ADNI study is an American large scale study on Alzheimer's disease. They have available a large data set with MR images of the brain. 

http://adni.loni.usc.edu

Most classification is based on machine learning: support vector machine, deep learning, extreme learning....