In our time and age, it is really hard to find a problem where machine learning is not already applied -- machine learning is practically everywhere, in business applications and science. Below is a short list of the maybe most common and intuitive examples:

- screening large molecule databases and identify which (drug-like) molecules are likely binding to a particular receptor protein
- predict the potency of a receptor agonist or antagonist
(In the figure above, I rendered a crystal structure HIV protease and some potential inhibitors, PDB Code: 4TVH)
Some interesting papers if you want to read more:
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Tarca, Adi L., et al. "Machine learning and its applications to biology." PLoS Comput Biol 3.6 (2007): e116. (http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.0030116)
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Lavecchia, Antonio. "Machine-learning approaches in drug discovery: methods and applications." Drug discovery today 20.3 (2015): 318-331. (http://www.sciencedirect.com/science/article/pii/S1359644614004176)
- find recognize input, find relevant searches, predict which results are most relevant to us, return a ranked output
- recommend similar products (e.g., Netflix, Amazon, etc.)


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predict if an applicant is credit-worthy
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detect credit card fraud
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find promising trends on the stock market
- handwritten digit and letter recognition at the post office
- voice assistants (Siri)
- language translation services
(Source: https://en.wikipedia.org/wiki/Handwriting_recognition)
- autonomous Mars robots
- identification of relevant information (objects) in large amounts of Astronomy data
(Source: https://en.wikipedia.org/wiki/Star)
- data mining of personal information
- selecting relevant ads to show
