Here are a few interesting things you can do using Python:
Web Development: With the help of Python develop of website with a back-end supporting REST API using python frameworks such as Django / Flask. Get started with Django Web Framework.
Data Analysis: Python offers different libraries, such as Pandas, Matplotlib,etc., to analyse data obtained either online or offline.
Web Scraping: Using Python's different libraries such as Requests, BeautifulSoup , Scrapy, you can scrape data from a website.
Machine Learning: Starting from predicting stocks, finger print identification, spam detection, to self driving cars, Machine Learning is taking over the world. Python is considered as the best programming language for Machine Learning and AI.
Automate a Facebook post: Cool things such as opening a browser and posting a Facebook status can be done using Selenium with python.
Build games: Develop a video game using Python's Pygame.
About using Python for Desktop Apps, I would say you can but this is not the best option. As Python is not created for to fulfill this purpose in the first place.