Holes in the heart: These are the most common kind of heart defects.  If present between the upper two chambers of the heart, they are called ASDs and if present between the lower two chambers of the heart, they are called VSDs.
Narrowing of vessels or valves: The main arteries leaving the heart may be narrow at a point or one of the 4 valves of the heart may not open completely.
Wrong connections of vessels with chambers:  Each part of the heart has a specific function. The left heart deals with receiving pure blood from the lungs and pumping it to the body. The right side of the heart receives impure (blue) blood from the body and pumps it to the lungs where with each breath blue blood becomes red and returns to the left heart. In certain heart defects (transposition, TAPVC) the vessels that enter or leave the heart are connected abnormally. Hence pure blood may end up going back to the lungs or impure blood may be carried to the body.
Malformed Chambers: of the 4 chambers of heart, 2 upper and 2 lower, any may be small and non-functional. Hypoplastic left heart syndrome is an example where the left sided chambers and vessels are small.