Hi,
I'm relatively new buy and hold investor (since 2011, have a dozen+ SFH rentals) so I'd like to see what others say. But for me, I look for positive cashflow to secure the property long term. I would be very careful on zero cashflow since there are always emergencies. If you don't have a positive cashflow, then you may not have built the reserves to pay for these emergencies (e.g. roof leaks, AC stolen, furnace breaks down, tree falls onto tenants car, tenant trashes the place during eviction). [I have had a roof leak (insurance covered, but still need to pay deductible), AC stolen (insurance covered but still need to pay deductible), tree fall onto my tenants car (turns out to be an "Act of God" but still paid the gardener to cut down the tree), and a tenant trash my place during an eviction.]
If I didn't have a positive cashflow on my properties and used it to build a healthy cushion, these situations would have been more stressful.
It's also important to look at what are you including in your expenses to calculate the cashflow. Are you including mortgage, property taxes, property management, insurance, maintenance, and vacancy? What percentages are you using for each of these factors? If your factors are too low, then you're actual cashflow maybe negative.
In summary, I use the cashflow to pay the expenses of the property, build a reserve so that I can hold the property over the bad times and have some passive income. Over the long term, I'll build equity as the tenant pays down my mortgage and as rents increase/house prices increase, my cashflow and equity will improve. A goal is not to lose the property because I didn't have enough reserves to pay for unexpected expenses.