The most common investment advice I see is to invest some fixed amount of money at a regular interval. E.g., 'invest $10000 every January 1st'. What does this actually look like with US stock market data? 

To see the results of this, I simulated investing $10000/year in the S&P 500 for 25 years starting in 1928, then again in 1929, and so on and collected all results. To handle inflation, I inflation-adjusted all values using the CPI. This includes dividends. Here are the distributions of account values vs years invested:

This spread is massive to me. Following the exact same investment algorithm, you could have ended up with anywhere from ~$200,000 to ~$1,200,000 after 25 years based solely on when you were born. 50% of the time, you'd have ended up with less than $400,000 or more than $900,000. The difference between $400,000 and $900,000 when it comes to retirement quality of life is enormous.

What are these in terms of annual yields? Here is the same thing converted to that:

The median is ~6%, and it's outside the 3-9% range a full 50% of the time. If you follow the general advice, historically you had a ~25% chance of a real return of <3% after 25 years of steady investing. I've posted similar but slightly different things here and here in the past if you're interested in seeing it visualized differently.

You're likely to do better with stocks than nearly anything else, they take no effort, etc. so definitely still invest in them. You're just as likely (historically) to be in the group that got >10% yields over 25 years than the group that got <1.5% yields. I just wish general advice included more about the uncertainty involved in this.