Can I connect high power LEDs in parallel without resistor?
It depends on what your design outcome is. No electronic components are created equal, they all have tolerances from manufacturing that make them different. If the brightness of the LED's is matched then the current needs to be matched. 

Example 1 and Example 3: The current through one resistor feeds two LED's, one LED has a slightly different I-V curve, it consumes more current and is brighter. The same thing happens in Example 3, it just has a constant current source. 

Example 2: The brightness is better matched  because either LED is getting a similar current. The currents won't be exactly the same however because there are still differences in the LED's

Example 4: This is the best way because the current has to be equal through both LED's, you will get the best brightness matching.







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