Thanks for the answers. I'm not very technical so I didn't know it came with a cooler.
Imran: The cooler that came with it. Seriously, there is no point in buying an aftermarket cooler for that processor, because that it not an overclockable processor. All Intel processors that are overclockable have a "C" or a "K" suffix at the end of its model number. So an i5-6600 is not overclockable, but an i5-6600K would be. Only the 6600K has the unlocked multipliers needed to be overclockable. Buying an aftermarket cooler for a non-overclockable processor is useless, as you'll never go beyond its default limits.
So if you do go for the 6600K rather than the 6600, you'll find that the 6600K is also slightly faster than the 6600 even in default configuration. And it's only about $5 more expensive than the 6600.
If you do go with an 6600K, then I would suggest getting the Cooler Master Hyper 212 EVO, or similar cooler. I have one right now on my system, and it's keeping the processor well below 30C, it's usually around 20C while not-overclocked, and it's usually in the same range even while overclocked.
If you don't care about overclocking that much, the Cooler Master 212 EVO is a good choice, granted you are going with the 6600K which doesn't already come with a CPU cooler (the 6400,6500,6600 come with one already).
The 212 EVO can handle decent overclocking and is one of the least expensive options out there, so for the average user it is a great choice. If you want something that can help achieve greater overclocks for maximum single thread performance, you may want to consider a 240/280/360mm AIO cooler, but of course this is a more costly option and depending on the expected usage at that point you may be able to get more out of an 8-thread solution such as the 6700K.
Hope this helps.
The 6600 comes with a stock cooler.
You don't need an aftermarket cooler unless you're going to overclock. Windoze put a patch in the OS which screws the system up if you're overclocking anything but the "K" series processors.
If you meant the Core i5-6600k, get the Scythe Fuma
Without knowing which case you're using (for clearance) or what country you're in (for pricing), would only recommend the low profile Cryorig C7.