I think it depends how heavily you're into those things. Do you game most days or just on weekends? Will the machine be used to dabble with photoshop and editing a home movie, or is it your 9-5 job?
For gaming, a fast cpu helps and most games can make use of multiple (2-4) cores. Having more than 4 cores for current games doesn't really get you any further. It's important to have at least 4-8gb of ram, usually 1600-1866 speeds are the sweet spot. A powerful video card is best for playing demanding current/new release games at higher resolutions and at smooth frame rates (60fps or better). You're looking at something like an r9 280x, r9 290x, gtx 970/980 or as good as your budget allows with typically 2-4gb vram.
For video editing and graphics rendering, a fast cpu with multiple cores is key. Quad core minimum, usually the more physical cores the better (6-8 core). This is where intel i7's really shine. Maybe an ssd for programs and large 7200rpm hdd's (2-4tb or more) for storage/working files. Ram, ddr3 1600 is probably fast enough and 16-32gb. A somewhat fast/powerful video card can help. Nvidia cards usually perform better because programs are optimized a little better for them unless it's a specific program like sony vegas where ati cards outperform nvidia and still do well with things like adobe premier.
Audio production you'd probably want to invest in a decently fast cpu, 8-16gb of ram, decent sized hdd's for storage of working files. I'm sure each program has it's preferred specs of equipment but it's likely not as demanding on hardware as video encoding or gaming and doubtful it demands much of a video card. Instead you'd want to invest in a high quality sound card with a variety of outputs and some really nice speakers.
Again it really depends on the level of use for any of these tasks. For the person who wants to change their car's oil a couple times a year, go to sears and buy a wrench for $6. No need to get a pro quality $60 wrench unless you're doing 10-20 oil changes a day.