Until the recent two years, no referral means no response whatsoever, for me anyway... referral usually guarantees I will hear back, even if it is rejection, all else equal, including the exact same resume of mine.

EDIT: Forgot to mention, I work for a bigg-ish Tech, and the bulk of the new hires are referrals. Very very few candidates get hired without referral. The referral fee is so high, the hiring manager is usually inundated with candidates the moment a role is available. Very seldom do we need to seriously consider non-referred candidates.

Some companies never respond so it could help get the first call. Maybe if two candidates are otherwise equal but one has a great referral it might help. At smaller companies it definitely helps, I definitely remember calling referrals to get eh scoop on people but that might not be as true at the mega corps.

At the very least referrals almost always bump you up the list. At best they can put you on the fast track for a position. IMO they are worth more than anything else you can do to get a job, so long as they are genuine.

Depends, if you have a specific enough referral to a particular hiring manager they could decide to stack the interview loop towards easy success