I always insist that people not email passwords or other sensitive data to me, or use instant messaging. Chances are good that your email or my email will someday get hacked, and one of the first things an attacker will do is search your mailboxes for words like "password", "account ID", and "credit card number". It's not a wise risk to take.
Here's what I do instead:
I usually ask people to use Keyvault which lets you send encrypted, short-lived, self-destructing messages accessible only by a unique key. The recipient receives a message form Keyvault with a link to the message referencing the unique key.
Of course this requires you to trust the people who make Keyvault to not be a bad actor. I'm not so worried about this because the service was recommended to me by a friend, Scott Paley.
You also have to trust Keyvault to handle their security properly, to really delete the messages after the self-destruct time limit expires, and so forth. So for the most sensitive data, I recommend sending the most sensitive data out-of-band, using one of the below methods.
This is a tradeoff of course; there's still a risk in trusting Keyvault, but it's a lot less risky than trusting your email provider.
I've thought about building an open-source version of Keyvault that comes with instructions for deploying it to your own personal Heroku installation, so that you don't have to trust anyone else.
This isn't as secure of an option as it once was, now that people can back up their smartphones to the cloud or to a computer, but if you don't identify what the password is in the text message I feel it's fairly secure. The way to do this is send an email that says "my account ID is ####. I'll text the password to you shortly." Then you just sent a text with your password, by itself.
For really sensitive stuff, like the passphrase to unlock your company's PGP keys, I write the sensitive data on a piece of paper, stuff it in an envelope, and mail it to the recipient, making sure they know to keep the envelope in a safe place.