Recently, Google has released a new version of Chrome that no longer trusts certain secure websites in a move to encourage those sites to switch to a different, more secure, security system. That's all well and good, except that about 80-85% of the World Wide Web still uses the old, but still good, system to secure people's connections to their websites.
When encountering these sites, you may now be presented with screens that look something like this:
Looks scary, right? However, receiving this message doesn't necessarily mean that you shouldn't trust the site. Also, it may not look obvious, but you can still reach the site you're trying to get to by clicking the "Advanced" link in the bottom-left, then clicking "Proceed to <website name>..."
I can't tell you which websites you can and can't trust. Every time you browse the internet there's a little bit of risk involved. Simply use your best judgement.