Office 365 has improved the sharing experience again in SharePoint Online. While I was preparing a presentation about 'Keeping up with changes in Office 365', I found the new simplified Share feature. Office 365 is always improving. Previously, if you wanted to generate a guest link you would have to email yourself. Now you can simply generate one using Get a Link. Get a Link is now more like sharing in SkyDrive for consumers.
Use Invite People to share with specific people and require sign-in.
Create an anonymous guest link. No sign in required.
Be sure the content you share is ok to share publicly. You can disable the guest link if you want to stop sharing the document publicly. But if you want more control, sending a link to specific recipients that requires sign in, it's best to use the Invite People option.