I want to glue my 4-year-old's LEGO bricks, but I want to be able to remove the glue when he is older. What is the best glue to use that is removable and okay to use on LEGO bricks?
Officially, LEGO Group doesn't recommend any adhesive on the toys. It can lead to corrosion or warping chemically, warping physically (the glue puts pressure on the pieces), and the removal of the adhesive also carries these risks. Plus, you'd be killing not only the the monetary value of the set, but the ability of those pieces to be active stimuli for creativity and motor skills.
The LEGO Movie clearly shows that using glue on the toys is what the villain does.
Your question doesn't explain why you want to glue the models for a 4 year old, so I'm going to go ahead and advocate that you don't glue and instead let your 4 year old build. 4 years old is a great time to be learning the fine motor skills, geometry, physics, colour and esthetics, not to mention creativity and storytelling. Gluing the models takes away their potential and makes Lego a blocky imitation of other toys.
Lego sells kits to 4 year olds (the Juniors line) that uses the exact same parts as the more complicated models in the other product lines. The main difference is build complexity; Lego Juniors use simple builds with few parts. With a bit of practice, your child should be able to handle the more complex construction of the other lines, which are typically set for ages 5 and up. That's only next year anyway.
There are three factors you have to consider here: the possible chocking hazard for your child, the possible toxicity of the glue to your child, and the degree of removability of the glue.
I don't think there exist a glue that is (1) completely secure (i.e. won't allow small parts to become chocking hazards), (2) safe to be handled and possibly ingested, and (3) completely removable for future play.
If I have to recommend a glue with the safety of your child in mind, I would recommend Super-glue. Once dry, it is non-toxic and it won't melt the plastic in the bricks. However, it is more-or-less permanent, which is important for safe playing time (and obviously doesn't meet condition 3 above).
I strongly recommend that you consider age-appropriate building toys, such as LEGO Duplo bricks. If you visit the LEGO Store, you can shop sets by age range to get an idea of what is available for your child.
As Nick says, LEGO System is probably not quite the right toy for a 4 year old. LEGO Duplo or possibly the new LEGO Juniors range would be better. LEGO obviously caution about the small parts on almost all System sets.
However, if you're looking for a temporary glue for now, then I'd probably go with a water based glue such as PVA that you'll eventually be able to soak off.
Be aware though, that this will not create as secure a bond as a permanent glue, so I would certainly advise supervising the play in case smaller elements come off.
If the goal is just to make the LEGO builds sturdier, and not straight unbreakable, I'd give a thought to the various food-based "glues", like sugar syrup (will probably become sticky to the touch as well) or flour paste. Both have the benefits of being 100% food-safe and water-soluble, while still providing a bit of adhesive force.