Some of the datasets in Kaggle are quite large.

Thank you Mr. Saptarsi Goswami.

I would recommend you to download data from "Pubmed" database and use it. To answer your another question, you can use Green Plum, Mongo DB or Apache Hadoop to process Big Data

Large unstructured datasets such as tweets can be best analyzed by hadoop.

One such dataset link is given below;

https://www.researchgate.net/publication/301790079_Sarcastic_processed_tweets

Data Sarcastic processed tweets

I think you can using text for analysis. It is easy to get using some kind of crawler....

if you would like to analyse a medical data you can use MIMIC data base to get whatever size you want . 

http://mimic.physionet.org/tutorials/install-mimic-locally-windows/

Thank you Mr. Amirah Alharbi  for your valuable information on Medical Datasets.