I usually use a plate chiller (pumping wort from boil kettle to chiller to carboy), but I have also tried recirculating the chilled wort back into the boil kettle until the temp in the boil kettle was below 120 or so. Then I would whirlpool, but like I've said, this didn't seem to work well.
This is what I used to do until recently. I've got a homemade version of the hop stopper that works pretty well, but after 15 min. of recirculating, it starts to get a little plugged. When I first start recirculating the flow is great. So I figured, I just need to drain the hot wort quickly out of the boil kettle into a second container. This would leave the hop debris and hot break behind in the kettle and then I could recirculate without worrying about debris. I use a modified corny for this purpose. I took the beer-out post off, removed the poppet, drilled it out a bit and pressed a plastic elbow onto it (needed to use a vise). I also had a lid with no pressure relief valve on it so I put another fitting there.
Now I gravity drain from the kettle to the corny via the beer-out post. I takes about 6 min. I'm going to replace the dip tube with some tubing of a larger diameter to speed the flow. Then I take the corny, hook the beer-out to my plate chiller, and the output of my pump to the fitting in the lid. I seal it up and apply a little bit of CO2 to the gas-in and the wort flows up and out, and down to my plate chiller. Once it gets to the pump and I turn that on and I can now recirculate to my heart's content. I put a liquid crystal thermometer strip on the corny so I can monitor the temp. I keep an tiny bit of CO2 pressure on to compensate for the contraction of the wort as it cools - the system is totally enclosed which also helps to keep out any possible contamination.
This of course can also double as a giant hopback (hops in a large bag), and the next time I do an IPA I'm going to use it to do a hop stand.
Plus, now if I forget to sanitize my fermenter before hand, or my yeast starter hasn't settled enough, etc., I can just let the now cooled wort sit in the corny until everthing else is ready