I have two recommendations:
1. Railroad Tycoon 2. This might seem like it's a little complicated for a three year old, but if you're going to be playing with him you might be able to ease him over the rougher(more difficult) parts. It's a train management sim with a big heart, and although I know not all kids are the same, when I first played it, it made me nostalgic for all the trains I saw and missed chances to see when I was little.
2. Sim Theme Park. Sadly this isn't on GOG yet, but I've heard of people getting it working on older computers(and some new ones) with a little help from the internet. There's tons of rides to build, a helpful AI which explains how to play and the people watching as they enjoy(or don't) your set-up can be priceless. Plus it might teach your child a sense of responsibility, or if not that, then some simple math. Trust me, if someone's not happy because you have one too few bathrooms in your park, they will let you know.

Trying to get Wildlife Park 3 for the younger ones.

Minecraft Adventure Mode (<- the perfect game!)

From GOG:
The Incredible Machine
Jazz Jackrabbit
Stardew Valley

Minecraft is beautiful and in adventure mode you can explore and build stuff without any monsters. You can't "fail" and just be creative. It's the perfect game for kids. Incredible Machine is about creativity, too. That's never wrong for for kids. It's just a bit confusing at first, but when you're playing together this shouldn't be a problem. Jazz Jackrabbit is a "slow" platformer. It's probably pretty hard for a 3 years old, but should be doable and a good training for hand eye coordination. You do shoot in this game and the characters are REALLY weird, but... well, it's a 25 years old 2D platformer...

Stardew Valley might sound like an odd choice, but most kids that age love stuff like "being a farmer". Just don't tell your kid about all the things you could or should do in the game (deeper mechanics). Kids are great at playing their own game within a game.

I second many of the suggestions people have already made, but I'd like to mention The Last Tinker. It's a single-player game, so he can't exactly play with you, but it's a very colorful game, really vibrant, the gameplay mechanics aren't complicated, even for a three-year-old, and if he finds some parts of it frustrating or difficult (the combat can be a bit too much for him), he can just watch you or his mom play it, and he'll enjoy it, as well -- it's like watching you play a cartoon, basically. It's also a pretty short game, so he won't get frustrated or bored by the length.

A friend of mine bought The Adventure Pals for her 6-year-old daughter and she loved the game, so that's another one I'd recommend.

He's also probably too young for it, yet, both in terms of understanding the humor and the writing, and in actually being able to play it, but he could probably still have some degree of fun by watching you play Psychonauts, maybe even trying some easier bits for himself.

Is Little Big Adventure the wrong age group? I thought it was a good kids game but no one said it yet.