Is there a report to show how many emails are sent to each person?

We've got something similar in our instance. It involved creating a new custom score field called 'Email Count'. A listener campaign was set up whereby if an email is delivered, add +1 to the count. Then, wait 7 days until 11pm, and minus 1 from the count. That way, at any given time you have a clear idea of the number of emails sent to that person in the last 7 days.  

If you don't have RCE, you'll need to create custom fields to track email names or counter fields to track number of emails sent - as suggested by Josh.

If you have RCE you can get such reports:

Count of Sent:

By email name:

The standard reporting options within Marketo are very simple and don't offer too much flexibility in terms of this. 

For clarity, are you looking for a total count (e.g. Email1: 3 emails; Email 2: 5 emails) or the names etc (Email 1: Newsletter, Webinar Registration, Webinar Reminder; Email 2 : Newsletter...)?

If you're looking for a total count, you could create a webhook that "counts" every time an email is sent and adds this value into a field within Marketo. This field could be wiped out each week, and values added to a Historical field so you can track previous weeks/months etc.

If you're wanting to identify the names of emails a lead has been sent, you could create a field within Marketo (e.g. Email Historical) that a Smart Campaign adds a value to every time an email is sent. That value could be the date and name of the email the lead has received. You could then create a Smart List of everybody who has had the "Email Historical" field updated in the past X days to see what has been run.

It's not simple, but these are the most straightforward options I could come up with.