Q:

Do other countries have the equivalent of Australia's Negative Gearing? 

Negative Gearing is a feature of Australian taxation where losses from real estate or share investments can be offset against assessable income.  
In simple terms, the difference between rent, and interest and maintenance fees for investment property can be claimed as a deduction on your income tax.  As a result, many individuals are heavily geared into investment properties in Australia.  This could be a major cause of poor housing affordability in Australia.     
Do other countries have such a system ?  If yes which countries and how does it work there? 

A:

I would say similar rules apply in the US.   If you have a net loss from rental property, you certainly can claim that loss against your personal income. 
There are various rules around this though that make it a bit less clear cut.   If you are a "real estate professional", which basicly means you spend at least 750 hours per year working on your rental properties (or related activities), then all losses are deductible against any other ordinary income you have. 
If you aren't a "real estate professional", then your rental income is considered a "passive activity" and losses you can count against regular income are limited to $25,000 per year (with a carry-forward provision) and begin to phase out entirely if your income is between $100,000 and $150,000. 
So, the law here is structured to allow most small-time investors to take rental real estate losses against their ordinary income, but the income phase-out provision is designed to prevent the wealthy from using rental property losses to avoid taxation.