Do you  collect  randomly? Complete subsets? Or just make a list of games that are good to play and work off that list?
I'm a mix of completely random and good game list. 

Working on a US SNES full loose set. Not really a subset, but thats what Im doing!

Building a personal collection of SNES loose carts. 109 + an SD2SNES on the list currently. 84/109 getting to the home stretch!

Basically I just tried to pick games I love and see myself playing 20 years from now. Carts I feel attached to and will likely never sell. I just go for NTSC; SD2SNES for the PAL/SFC/rom hacks.

NES games with battery backup—just the ones I want to play though.

Been chipping away at nes set. I restarted this past fall at am approaching 200. Trying to wipe out all the R1 and 2's: have 36 more. Been trying to grab as many uncommons as I can

First run (or day 1), or unusual hardware revisions of things that are significantly different from the rest of the consoles life. Like the Multi A/V out from the SNES- GC on the NES toploader, or the myriad of colors on the N64
kind of an odd one I know but it makes for interesting extras on the systems.
so far I have:
Green and Smoke N64's
Square Button Famicom Complete in box
PSX SCPH-1000 and SCPH-1001
2 launch day japanese Saturn consoles almost complete in box with Reg cards and receipts
Nes Top Loader
SNES jr
SFC with SHVC sound and Cartridge lock

just kinda odd ball hardware like that, with some significance

im collect randomly

So far I'm chipping away at my Smash Amiibo set (10 left until the complete set!) and then I'm exclusively going to focus on 3DS and GBA. Full set for 3DS, and random CIB games for the GBA that are both affordable and in good condition.

I'm trying to go for a complete Sega collection, Saturn's gonna be fucking expensive.

Trying to CIB my Gradius collection. Only missing the box for Interstellar Assault, and box and manual for 1 and 3. Pain in the ass. Not sure where to after that, probably going to start saving up and plop down a huge load on Mega Man.

Mid-tier (50-100$) CIB SNES titles I'm missing. After that need to fill in the Mega Man X3 gap that taunts me whenever I look at my collection spreadsheet.

Right now I'm looking to box my n64 games from when I was a kid. Then after that i dont know. Maybe all the genesis hockey games cib

I have a few different goals at once. I want to complete the zelda set and get my childhood n64 games CIB. Other than that I am looking for SNES and n64. In all honesty it is a very random process. New things jump out at me. My next one is hopefully earthbound.

Definitely random.

working on having the Top 30-40 GameBoy titles (sorted by rarity) sealed and VGA graded ;-)

VERY casually looking for boxed gradius, tmnt and final fight to finish. Collectively between all 3 I only have like 5 games left, just not in a hurry to finish 'em I guess haha.

The megaman series on NES. Currently only have 3 which is easily the most common one.

NES light gun games only need a few more

Working on snes RPGs

US TG16 hucard and cd games

nes licensed set

No huge rush just chipping away when I find decent deals. Not really collecting anything after the 16 bit era.

I'm an RPG collector so I'm chipping away at my RPG collection. Anything I get in lots while I'm doing that for my larger NES, SNES, N64 or Genesis collections are a bonus.

I'm always working on collecting all the RPGs.
I don't even have all the Final Fantasies or Dragon Quests yet so I've got a long way to go. I'm also working on collecting the Working Designs titles. And the Shining series. And the Tales of series ... etc.

Blockbuster Exclusive Games, my criteria is that it has to have the logo on the front, for example:

CIB Capcom NES subset. 3 boxes, 8 manuals to go.

pretty much random

This is what I do as well because as a kid I always felt I got more bang for the buck with RPGs.

Playing them now most of the extra time was grinding lol but hey still my favorite genre.