Stir together the water, sugar and pickling spice in a medium-size saucepan. Bring to boiling. Lower the heat, simmer, uncovered, without stirring, for 5 minutes. Cool to room temperature.
Slice the zucchini, carrots, sweet red peppers and yellow squash. Place in a large bowl. Pour the cooled pickling liquid over the vegetables. Cover and refrigerate for at least 8 hours or up to 3 days.