CentOS/RHEL has a similar tool called ABRT. Its primary function is reporting the issues to RH bugzilla (or customer portal), but you can also configure it to send an email or just let it collect logs and core dumps for manual analysis without reporting anything. There is a chapter about ABRT in the RHEL documentation, but the basics are simple: install `abrtd` (and start the `abrtd` service) and the `abrt-cli` or `abrt-desktop` if you are using GUI.
If you want to debug a crashed/non-booting system, you might also want to take a look at sosreport which is used for collecting logs and configuration details.