What is the maximum length of a Push Notification alert text?

The real limits for the alert text are not documented anywhere. The only thing the documentation says is:

In iOS 8 and later, the maximum size allowed for a notification payload is 2 kilobytes; Apple Push Notification Service refuses any notification that exceeds this limit. (Prior to iOS 8 and in OS X, the maximum payload size is 256 bytes.)

This is what I could find doing some experiments.

• Alerts: Prior to iOS 7, the alerts display limit was 107 characters. Bigger messages were truncated and you would get a "..." at the end of the displayed message. With iOS 7 the limit seems to be increased to 235 characters. If you go over 8 lines your message will also get truncated.
• Banners: Banners get truncated around 62 characters or 2 lines.
• Notification Center: The messages in the notification center get truncated around 110 characters or 4 lines.
• Lock Screen: Same as a notification center.

Just as a reminder here is a very good note from the official documentation:

If necessary, iOS truncates your message so that it fits well in each notification delivery style; for best results, you shouldn’t truncate your message.