There are a multitude of apps available for shapes and colors. 
The shape app that is the most fun is Giggle Spittles. Giggle Spittles are three alien creatures that drop down from a brick wall. As they drop they they make a whizzing sound and then a bouncing sound when they hit the ground.  There is a different shape on the belly of each Giggle Spittle. The shape on the alien needs to be matched with the shape that appears on the brick wall. The child needs to touch the belly of the alien that matches the shape on the wall. When the alien’s belly is touched, the alien laughs, the belly distends, and the alien belches out the shape. The child moves the now floating shape onto its matching shape on the wall.  After the child has successfully matches the shapes, the screen automatically changes to scene with a animals. The child is instructed to touch a specific shape found within the scene. The free app is limited to circle, square and triangle. More shapes are available for $1.99. Ages: 3+. Rating: ++++
Shapes by presents four shapes—circle, triangle, square, rectangle—as photographs of common objects, such as a stamp for square, a slice of pizza for triangle and so on. Accompanying each frame, is the narration, “The ____(name of the object) is ______(shape).” I like the association of shape with a real object. However, some shapes are inaccurately named and thus can mislead. For instance, 2 dimensional shapes are named as one dimensional:  a road cone is presented as a triangle, a typewriter as square, and grocery bag full of groceries as a rectangle. I prefer that a goal be worked on as cleanly as possible. By that I mean that if the child needs to learn the names of basic shapes, then drawings of shapes are sufficient. If one wishes to draw associations between common objects and shapes then this app is the one to use. Ages: 3+. Rating: ++
Kids Place has two free apps for colors: Baby Hot Air Balloons and Baby colors. The apps teach colors using either balloons or hot air balloons that appear out of a heavenly horizon and bounce around on the screen in the sky or above a beach and blue body of water. Depending on the app clouds that look like genies float across the screen, different colored bubbles shoot up in geyser like fashion out of the sand or sky, float around, or erupt in a sphere before they disappear and the process starts over again. The background also changes with zen like environmental sounds and musical accompaniment. The effect is somewhat mesmerizing. Tapping the screen changes the color of the balloon. The narrator speaks with a British accent. Free when I downloaded them, these apps are now $.99. Ages: 2-4. Rating: ++
Shapes and Colors offers learning in Chinese or English. Colors are presented in a variety of different shapes. The app has learn and play options. The learn option presents a color highlighted by an object of that color and 8 shapes below it. The word for the color is written in English and Chinese. The play option has 24 shapes and colors on the screen. A voice says, “Please select the _________ blocks.” The blank is either a color or shaped named. The child has to then tap on all the shapes, among the 24, of that color or shape named. There is a visible timer that counts down from 120 seconds to 0. Thus, the child needs to work as quickly as possible finding all the shapes or colors named. The instruction varies throughout the time available. The child’s score is visible on the screen as he/she works. Once the game is completed, a screen appears allowing the child to build a picture on an empty screen using a variety of different objects.  Or, one can click the x and return to the main screen. This app is free. Ages: 3-6. Rating: +++
Abby The Train Driver, by developer CF Corp, instructs the child to tap on a toy of a specific color. Tapping on the correct color, transfers the object to a train. The train waits until each of its three wagons has an object before it chugs away. The settings option allows one to select the minimum number of toys to display (1-4 on the free version, up to 10 on the $1.99 upgrade) and the colors (there are 11). Fortunately, one can opt out of the music and sounds that can be distracting and annoying. Ages: 2-4. Rating: ++
Baby Shapes, by GrasshopperApps, offers different colored silhouettes of common and inventive shapes such a lightening bolt and shamrock, making this a vocabulary app as much as a shape app. The settings option allows one to select the minimum and maximum number of items to display and customization of items and sounds. One can also select from a library of shapes to display. This app was free when I downloaded it, but is now available for $.99. This is a nominal price to pay for a creative app that allows beyond the presentation of simple basic apps. Ages: 3+. Rating: +++
Speak Colors, by RWH Technology, offers seven basic colors–black, blue, green, orange, red, white, yellow. These colors appear at the top of the screen. Tap on a color and a big square turns that color. Next to the colored square is a picture of a common object of the same or similar color (a vibrant blue square was demonstrated in the form of a light blue dress). If one taps on either square, an audio setup button appears. Tap on the green arrow and hear a dull sounding voice name the color or object. A better option is the exclamation point button. It allows you to record your voice naming the color and object. This app is free.
Ages: 2-4. Rating: +