Seeing the games they review/collect/comment on?
Not missing a new release from them when they publish it?
Some other reason?

For me, it's their devlogs. I find people's progress on their games to be quite interesting.

Like Bynary Fission said above, getting to see people's devlogs is a big reason for me.

But I also follow people as a way to say "Hey I like your stuff", and so that I see what they're doing/making/following/etc. in my feed.

I mainly following folks as a way of supporting them at first. After that, I mainly care about the email I get whenever they release something new.

I follow someone here just to see if they release a new game.

I like their creative or cute aesthetics. 

I sometimes follow based on a game they made and how communicative they are about it.

When following a dev it's usually because A. I like their work. B. I want to see the progress on a project that interests me or C. I want to support them in a small way and keep updated on what they are up to.