My suggestions are Inherit the Earth, The Night of the Rabbit and the Lego games.

Goblins worked well with my kids. Not quite that young, but 5. They couldnt complete the puzzles without me assisting but it fun for them to watch the actions and its all point and click.

The recent thread on the same topic:

http://www.gog.com/forum/general/kidfriendly_games_help

There are some good suggestions in there.

Some of the easier point-and-clicks with voice acting might be good for you to play through together. You can ask things like "Should we press the button?" or "What would happen if we put the fish in the toilet?" (Toonstruck reference) to have her feel that she's helping.

The hardest part for most PC games that aren't specifically designed for preschoolers is that they usually can't read yet. When my own girls were that age, I found that they did do pretty well with some of the casual hidden-object games, especially the ones that give the outlines of the objects you're trying to find.

ANYTHING with Putt Putt on it.

Or ANY sort of point and click adventure for that matter, they are basic, easy to get into, and most of the genre is covered with shovelware with games for kids, so you'll never get the end of it with your child.

Prehistorik

Only spacebar and arrows need it to play.

Don't know if you're into adventure games, and while your daughter is only four years old, you might want to check out A Cat's Night which was made with the AGS Engine for (school) kids. Here's the AGS page, and here's a walkthrough.

There's also a sequel to it, A Cat's Night 2 (AGS page).

The games are free, and if you decide that they're not suitable for her yet, you might want to keep the links and introduce them to her in a year or two.

Sorry, didn't mean to be annoying, it just seems like so few people are actually paying attention to the OP.

I'm surprised that no one here has mentioned Wacky Wheels yet. It's definitely kid friendly with it's cute animal drivers and colorful race tracks. Also, there is the option to play two player split screen (on a single keyboard) so that you can enjoy the game together!

GOG had a puzzle bundle last November. It included:
http://www.gog.com/game/blocks_that_matter
http://www.gog.com/game/tetrobot_and_co
http://www.gog.com/game/qube_directors_cut
http://www.gog.com/game/mousecraft
http://www.gog.com/game/clarc

Easily the best bundle I've seen from GOG. My son was four at the time, and he loved all five games. I was at the controls, but he sat on my lap and made suggestions. Sometimes he would have ideas up front. It was important to try them out, even when I understood that they wouldn't succeed. Often, it was possible to reduce the puzzle to something he could manage by placing a few key pieces. CLARC didn't really invite his particpation like the others did, but he enjoyed chattering through it nonetheless.

I'm not four years old but I think you sold me on Blocks that Matter anyway.

It's an excellent puzzle game.

There are some frustrations, including some racing (effectively timed) situations, and some flagrant fire-dodging bullshit. If you're happy to play three or four levels imperfectly just to get past them, though, you'll enjoy the game. Thinking puzzles dominate. The twitchy puzzles are only a small part of Blocks That Matter, thankfully.

Did somebody say...
https://38.media.tumblr.com/8532fff79925c630d5c361560cf8f717/tumblr_njxejpmnrT1s2yegdo1_r1_400.gif
...PUZZLES?!
I sadly haven't played the game yet, having only just bought it, but when I do, I'll come back to this thread and let y'all know.

As wiki says, the word buff is used in its older sense of a small push and the game is sometimes aslo called <i>blind man's bluff</i>..
I'll add Hopscotch and Chinese jump rope/elastics to the list : )

Gosh, so many replies, it's a gold mine! thanks everyone and merry Christmas to you all :)

We had a lo of fun with Tom & Jerry - War of the Whiskers.

The simpler the better. 2D platformers are probably best.