You will not have access to your EOS after June 1st 2018 if you do not register.
Genesis Campaign - Register your EOS!
What is EOS registration?
Registration or "Mapping" associates your ethereum wallet with a EOS public key. Your EOS will only be accessible on mainnet if you do this. More on these terms.
How can I check if I have completed registration?
It takes 2 minutes to check! Find your ethereum address and then use the EOS Registration verification tool
How do I register?
There are several guides online. There are also YouTube videos. The best guide is probably the one from Sean Mitchell at Block One.
When should I register?
Register now. ERC20 EOS tokens are frozen 48 hours after June 1, 2018 at 22:59:59 UTC.
What happens if do not register?
You will not have access to your EOS after June 1st 2018 if you do not register. Proposals exist but nothing is developed yet!