I have 1600 dollars to build a gaming PC,

Go to http://www.pcpartpicker.com and choose the latest components according to your budget. Its easier and better to choose it on your own.

$1600 with or without OS and monitor?

May I suggest looking at your Laptop .... Perhaps adding a SSD would improve your experience.

Also - Somewhat related - I had an Asus that with WIndows 10 - was seeing my hard drive as an SSD and would not perform defrag. Moved it to another PC and ran defrag - it improved the laptop experience greatly. Not quite to the point of replacing it with and actual SSD - but I did this last year with my wife's netbook - and it made a useless piece of technology workable.

There are numerous ways to do this. If you're coming from a laptop, my guess is you need a monitor, OS, keyboard, and mouse. Let's figure $150 for a 1080p monitor, $90 for the OS, and $100 for a nice keyboard and mouse. That makes your $1600 budget breakdown a bit:

$150 Monitor
$90 OS
$60 Keyboard
$40 Mouse
$1260 PC

Now you've got a better idea of what you can get. Next, let's choose some basics: the case, the GPU, and the storage. Let's say that you want a 250GB SSD + 2TB WD Red drive, which are $83 and $90 respectively so that's $173. The case, let's figure $100 for something nice. This leaves $1000 or so, a bit less, for the GPU, PSU, Motherboard, CPU, and RAM.

Let's say you end up with a 60Hz 1080p monitor, then a single R9 390 would be way more than you need and should work well for years. That is about $320, leaving you this:

$150 Monitor
$90 OS
$60 Keyboard
$40 Mouse
$100 Case
$80 SSD
$90 HDD
$320 R9 390
$670 CPU, RAM, Motherboard, PSU

Now we have a couple choices: Skylake or Haswell. If we go with Skylake, then I'd suggest something like a $150 Z170 board (perhaps an MSI Krait), an ~$85 16GB (2x8GB) DDR4, and something like a $75 550W eVGA Fully Modular PSU. That would leave $360 for the CPU.

Now $360 for the CPU could basically get you any Skylake. However, I'd suggest if you want to overclock that you have the Core i5-6600K + $100 liquid cooler, like the Corsair H100i. That CPU is about $250, so this works out rather nicely.

If you go with Haswell, then you'd need DDR3 RAM, a Z97 board, and a Core i5-4xxx or Core i7-4xxx chip, like the Core i7-4790K or the Core i5-4690K. These boards will have no new CPUs ever made for them, and the DDR3 will not be usable in newer motherboards. This isn't necessarily a bad thing, as odds are that by the time you'd want to upgrade if you could use the same RAM then it would be notably slower than modern RAM and if you could use the same board it would be notably out of date (eg, missing new features). For example, my motherboard doesn't have USB 3.0, PCIe 3.0, or SATA 6Gbps, so it's entirely likely that we'll have something else in a few years that isn't available now and you simply can't future proof. Hence, a Haswell build is not necessarily a bad thing because the main argument for the Skylake build is the ability to upgrade. I would argue the main benefit to Skylake is the ability to utilize 32Gbps PCIe 3.0 x4 M.2 SSDs.

PCPartPicker part list: http://pcpartpicker.com/p/k6y93C
Price breakdown by merchant: http://pcpartpicker.com/p/k6y93C/by_merchant/

CPU: Intel Core i5-6600K 3.5GHz Quad-Core Processor ($253.89 @ OutletPC)
CPU Cooler: CRYORIG H7 49.0 CFM CPU Cooler ($34.50 @ Newegg)
Motherboard: Gigabyte GA-Z170XP-SLI ATX LGA1151 Motherboard ($125.99 @ Amazon)
Memory: Crucial Ballistix Sport 8GB (2 x 4GB) DDR4-2400 Memory ($45.99 @ Adorama)
Storage: Crucial BX100 500GB 2.5" Solid State Drive ($169.99 @ Adorama)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($46.89 @ OutletPC)
Video Card: MSI Radeon R9 390 8GB Video Card ($319.99 @ Newegg)
Case: NZXT Phantom (Black) ATX Full Tower Case ($109.99 @ Newegg)
Power Supply: EVGA 750W 80+ Gold Certified Fully-Modular ATX Power Supply ($99.99 @ Amazon)
Total: $1207.22
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-02-01 11:20 EST-0500

I read some of what the guy said above me and I assumed that you would also need to spend about $400 of your budget on monitor, OS, keyboard etc so I took that into account. You can tweak this build to your own personal preferences of course. If that $1600 ends up not including the monitor, os, keyboard, and mouse, then you can upgrade the videocard to something else.

If you don't want that much SSD storage, you can lower it to a 250gb drive, and upgrade one of the other components. You are more than free to pick out whichever case you personally like but this one has some beastly reviews. Getting 16gb of ram may not be a terrible idea either. Up to you.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-6600K 3.5GHz Quad-Core Processor ($253.89 @ OutletPC)
CPU Cooler: CRYORIG H7 49.0 CFM CPU Cooler ($34.50 @ Newegg)
Motherboard: Gigabyte GA-Z170-HD3P ATX LGA1151 Motherboard ($87.98 @ Newegg)
Memory: Crucial 16GB (2 x 8GB) DDR4-2133 Memory ($64.99 @ Newegg)
Storage: Crucial BX200 240GB 2.5" Solid State Drive ($63.99 @ SuperBiiz)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.89 @ OutletPC)
Video Card: XFX Radeon R9 390X 8GB Double Dissipation Video Card ($349.99 @ Newegg)
Case: NZXT Source 210 Elite (Black) ATX Mid Tower Case ($43.99 @ SuperBiiz)
Power Supply: SeaSonic S12II 620W 80+ Bronze Certified ATX Power Supply ($64.99 @ SuperBiiz)
Optical Drive: LG GH24NSC0 DVD/CD Writer ($13.89 @ OutletPC)
Operating System: Microsoft Windows 10 Home OEM (64-bit) ($87.95 @ OutletPC)
Monitor: Acer XG270HU 144Hz 27.0" Monitor ($453.99 @ Mac Mall)
Keyboard: Cooler Master CM Storm Devastator Gaming Bundle Wired Gaming Keyboard w/Optical Mouse ($24.99 @ Micro Center)
Total: $1595.03
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-02-02 00:26 EST-0500

(include $55 rebates)

not exactly the BEST components, but they are all very good. gives you everything you need and nothing more. 1440p @ 144Hz with FreeSync and a r9 390x to power it. the best experience you can buy at that budget.

this seems like a good build at first glance, but if you think about it... you're pairing a gtx 980ti with a single 1080p @ 60 Hz display. thats way overkill. its going to max games without breaking a sweat, leaving you with alot of potential power that isn't being realized in any way. a gtx 980 could do the same for $200 cheaper.

if you go with a 980ti you will probably want to run a higher resolution... maybe 3 1080p dispalys, or a high refresh 1440p, something along those lines. or else its pretty much a waste of money to spend so much on that GPU

I don't think it's a waste rather, it's an investment which assure you that games will run just fine at future. After 2 years, a single 980 ti may struggle to play games at 1080p resolution at max settings, In that case definitely better than a single 980.

Now you know the actual reason for this suggestion.