
* Draw a rectangle/square WITHOUT a stroke
* Copy it and fill each shape with the desired colors
* make sure they are perfectly aligned - window > align
* Scale them down to the size you would like them to be in your art
* Drag them into the swatches palette
Now you can fill any shape with your new pattern swatch
You can make your stripes horizontal or vertical depending on how you arrange the rectangles/squares
CHECKERS

If you used squares to make your stripes you can copy and paste the two squares and rotate the copies 180 degrees with the rotate tool. Double click on the rotate tool and enter in the degrees for a perfect rotation. You can select "copy" in the rotate window if you didn't copy and paste yet. Line evrything up perfectly and drag it into your swatches palette.
Don't forget NO STROKE!
POLKA DOTS

Draw a square and then a circle. Use the Align Palette to align them perfectly both horizontally and vertically. Add some detail like strokes or layered circles if you want.
POLKA DOT with DIAGONAL REPEAT

You can use the same swatch that you used for the simple polka dot. You just need to add another circle that you must first divide into quarters.
* Hold shift and use the line tool to draw 2 lines as shown

* Select all thre objects and align them vertically and horizontally
* Window > Pathfinder - Click on the first icon on bottom right (divide)
The lines will disappear!

* Object > Ungroup
* Now position each quarter into each corner of the pattern swatch. See Above!
Remember - NO STROKE
Try something creative with the patterns described above