One way to engage a child in science experiments is to show them how day-to-day activities involve science. Cooking -- especially baking (which generally requires precise measurements) -- is an excellent place to start because several of the basics of experimentation (including measurements and following directions) are involved in food preparation. For example, you can take a recipe and "experiment" on it by adjusting a certain amount of an ingredient. Ask the child how he expects this adjustment to change the overall taste and texture of the meal.
Another way to engage children in science is to show them that everywhere in nature, even the backyard, is ripe for experimentation. Have a child play a game in the backyard where she counts the number of different plants and animals she can find within a certain time span (e.g. one hour). Repeat the game at a different time of year and a different time of day. Ask the child what factors she believes affected the different counts.
Many kids have an inherent love for astronomy because it is so different from what they experience on a daily basis. You can take advantage of this wonder by developing astronomy games. Similar to the backyard game, you can use a telescope (or just the naked eye) to observe stars and constellations every night over a one-month span. Explain to the child why the stars appear to move and why certain stars can only be seen at certain times of year.
The human mind itself is ripe for potential in doing science experiment games for children. Put together a simple memory test, such as matching flash cards, and then have the child time himself to see how long it takes him to match all the cards together. Slightly adjust the experiment, such as using a different set of cards or doing the experiment at a different time of day. This is a good exercise to show a kid how subtle changes can make major differences when doing a science experiment.