I pick a genre I'm in the mood for, find a game that fits it, and play it.

Fortunately, my backlog is small. Having said that, recently I've been preferring to replay my good old favorites instead of tackling my backlog XD

lol I have a hard time. I usually end up spending more time on games I've already completed, i.e. Bloodborne/DS3. So it takes me much longer than it should to get through my backlog. 

Shortest games first. That way you can get it out of the way quickly and move on to the next one.

Tagging.

#1 - Play games. Don't think about it, just turn on the console.
#2 - Grab a game from the collection. No analysis paralysis BS here, grab one.
#3 - No trophy hunting, new game+, or perpetual multiplayer. Keep moving to the next.

I only have a few games in my backlog, maybe 4 I think, I don't mind if I end up not playing them but they are for a drought but since I will buy a Scorpio at the end of the year, that might grow a bit picking up at least 8 games I missed including the master chief collecting and rare replay, which take up quite some time lol.

Also its a good year for games, if my backlog grows beyond 10 games I generally stop buying games until its below 5 again, for me that worked well in the past with PS2 and Dreamcast I always try to play the worste games first lol

Most times I just pick it up randomly and play it. I always stick to the main story and if the game still has my attention i'll do the side quests after, if not I just move on to the next game.

My backlog at this stage contains more games to play than I have life left to live I think. It wouldn't be possible for me to finish them all so all I do is buy more and enjoy those I do get a chance to play and those I don't I enjoy having a lovely collection of games.

Same here. I've gone mostly retro, aside from a few select titles each year...

And then I also buy most of what Nintendo puts out, because they are the most consistently solid publisher on the planet. Even their worst years, they end up the the top 3 reviews-wise.