$700 build, I've used PC Partpicker, so different shops:
PCPartPicker part list
CPU: Intel Core i3-4170 3.7GHz Dual-Core Processor ($112.89 @ OutletPC)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($19.89 @ OutletPC)
Motherboard: Gigabyte GA-Z97-HD3 ATX LGA1150 Motherboard ($79.99 @ Newegg)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1866 Memory ($39.99 @ Newegg)
Storage: Seagate Barracuda 2TB 3.5" 7200RPM Internal Hard Drive ($67.88 @ OutletPC)
Video Card: Gigabyte GeForce GTX 960 4GB Video Card ($202.98 @ Newegg)
Case: Antec P70 ATX Mid Tower Case ($37.99 @ Directron)
Power Supply: Corsair CX 600W 80+ Bronze Certified Semi-Modular ATX Power Supply ($44.99 @ Newegg)
Operating System: Microsoft Windows 10 Home OEM (64-bit) ($89.88 @ OutletPC)
Keyboard: HP Wireless Classic Desktop Wireless Standard Keyboard w/Laser Mouse ($15.99 @ Amazon)
Total: $712.47
It's bit over the $700, I felt $13 is not enough to cut corners (though some have already been cut), but 1TB storage instead of 2TB will put it under $700 if that's the problem.
CPU: I went with i3 since I think it's still better option than AMD 6300/6350, hyperthreading in i3 still manages to keep them performing quite well, plus upgrade path to i5/i7 is always an option later.
CPU cooler: 212 is preferred bang/buck solution - not enough budget for Noctua, not that one is really needed here.
MB: I tend to only go with ASUS and Gigabyte, GA-Z97 was cheaper. Not very fond of ASRock, but for people who don't have problem with them, you can save some money here.
RAM: Would rather pick Kingston, but this one is quite cheap for 1866 and CAS 9 memory
Storage: Seagate is not something I would usually put in rig (WD guy here), but it's fairly good HDD with 2TB capacity - I just think that 1GB gets filled up pretty quick
GPU: It comes down to AMD 380 or nVidia 960 - they perform about the same, but in this gen nVidia usually had less problems with some of the games (though they and their Gameworks are the culprit in the first place). 4GB is maybe not really nessecary, but I felt that it's beter to have it for a small price difference - some $15 can be saved here if 2GB card is picked.
Case: I tend to like Antec's cases, it's not Fractal Design, but it gets the job done in this build.
PSU: This is quite popular budget PSU, I would rather see SeaSonic, but budget contrains and all that.
OS: It is what it is.
KB/M: Wirelles combo, nothing special, gets the job done.
@JEMC I really think you need to put some aftermarket CPU cooler there, 6300 stock fan is loud as hell.
Essay Pro