Depends on your goals and how much time you have.
I own single family rental homes in nice neighborhoods. Not the best cash flow, but good tenants and not too many headaches. I had one house paid off and I ran the numbers on a spreadsheet to see if I should keep it with no mortgage, keep it and do a cash out refi, or sell it and use the proceeds for down payments on multiple properties.
Selling and buying several properties with financing would have been the most profitable, but it would have also required more effort up front (selling then buying/leasing several properties).
Continuing to own the property with no mortgage would have allowed me to get great cash flow, but the return on investment was low. In this case the rent is about $2,000/month, and I could have walked away with about $400,000 if I sold. Cash flow when the house was paid off was around $1700/month. Return on investment in the next year would have been whatever % the house increased in value plus the amount cashflow in the year minus any expenses/reserves I would expect to need for future capital expenses ($1700*12-$5000 saved for future capital expenses) / $400,000 = 3.8%. So if the house prices appreciated 10% in the next year, my return on investment would have been 10%+3.8% = 13.8%. Not bad but that is assuming house prices go up 10%. If house prices go up 3%, my return on investment would only be 3% + 3.8% = 6.8%.
I like to make fairly conservative estimates of home price appreciation. I look for rentals where I project about a 20% ROI if the house appreciates 3% per year. To get to 20% ROI it's helpful to have financed properties because it is easier to get 20% profit out of one house if you have a smaller amount invested. In the example above, I did a cash out refinance and pulled out $330,000. Since I could have sold the house and walked away with $400,000, I left $70,000 invested in the house when I refinanced it and took $330,000 in cash out.
Now my mortgage/taxes/insurance costs me $1900 per month, the rent is $2000 per month so my cashflow is $100 per month, and in reality my cashflow in negative if I factor in expenses including saving a few hundred dollars a month for future big expenses like the roof. On the other hand, I have $330,000 to do other things with. The return on investment for the $70,000 I still have invested in the house much is higher:
Total ROI=ROI from rent-expense+ROI from house price changes
Return on investment from rent - expenses = ($24,000/year rent * 12 - $14000 mortgage interest - $3600 taxes/insurance - $5,000 cap ex) / $70,000 invested in the house = 2%
Plus the return on investment if the house appreciates 10% ($40,000 on a $400,000 house) = 40,000/70,000 = 57% for a total ROI of 59%
Or if we assume the house appreciates 3% ($12,000) -> $12,000 / $70,000 = 17% plus the 2% ROI from the rent = 19%
In my case, I have other income sources right now and don't need the cash flow. My goal is building wealth long term. For me, keeping the $400,000 tied up owning the house free and clear and making 6.8% ROI did not seem attractive. I could probably make more money on average investing in an index fund and I wouldn't have to manage a rental.
I decided to pull cash out of the house, so I could make a higher ROI on the $70,000 I left invested in the house. I took the $330,000 and invested it elsewhere.
If you need the cash flow now because you don't have as much other income coming in, you may decide to buy fewer properties with less financing. If you don't need the monthly income now, you would probably get a better long term ROI by buying more properties with financing.