To elaborate a bit most big email clients are fairly hardened against it. It could be that the client has a bug in that eventually allows execution from a malicious email, one that somehow slipped through all the nets, but that would be something special indeed.
I can't say I have been paying attention but I have not heard of this happening for a big client in a decade or more (and I think even that was someone's ill fated attempt to give email the ability to see flash objects). If you are really paranoid you could also do a text only thing and that would be impressive indeed for something to punch through that. If you run some no name client or ancient fork of something then it becomes more of a thing.
Clicking bad links or running attachments is what gets people in trouble. The worst realistic thing to happen from simply reading an email would be if they put a remote image in there which in turn confirmed an active account or something boring like that, and for what it is worth most clients will block remote images if you want them to.
Yes, my mom was a recent victim of this on her Comcast email. I don't know entirely how it came about, but she opened an email, and a few hours later, some dickweed Chinese hacker changed her Amazon email and password. To make it worse, the customer service reps at Comcast told her "Amazon doesn't support Comcast email derr herr herr". So she called Amazon and they weren't helpful initially, an hour later, her account was finally restored. So yeah, emails can royally screw you over. We knew it was a Chinese hacker as the email had a Chinese name in it.
If you use an online email client (gmail or outlook online) with an up to date browser (firefox or chrome) without any dodgy browser extensions, you pretty much 100% safe.
If there are exploits in the software used to display the email on your computer you could be in trouble, but browsers are very safe these days - so long as you don't install extensions or fall for phishing.