Overheating when idling

Thank you for the information. If you wouldn't mind I would like to go into better detail just so you have a better understanding. The car is a 2002 Honda Civic LX with about 150,000 miles on it. The first sign of overheating actually happened in the city, stuck in traffic. It seemed to be overheating while idling. I went and bought a new thermostat. Problem went away for a while. Overheating came back, only while idling or the car just sitting or at low temperatures. Bought a radiator and a radiator cap and replaced both. Problem was still there. Replaced the clamp that holds the main hose, thinking that was the problem because it looked damaged. Car ran fine for about a month. Then started overheating again. I removed the thermostat about a week ago thinking the weather is warm, I don't need it and maybe it was a faulty thermostat all along. Been driving fine for 2 days without the thermostat, now it's over heating again! I went and replaced the temperature sensor, still overheating. When it overheats there is no smoke. The cars temperature gauge just climbs up all the way up to the red, to the max temp. No smoke, no sweet smell, I feel like the fan is kicking on but not always. Not every time the car overheats. No milky discharge in my oil. No visible leakage of coolant under the car or tailpipe. I'm at a loss for words. I don't know what else to do. Please help!

I did check the water pump by taking the radiator cap off and gave the car gas and it sucked it in. What else should I be checking about the water pump? The fans do kick on it.