information from
http://www.pilatesinsight.com/pilates-equipment/pilates-reformer.aspx
http://www.stottpilates.com/faq.html#anchor_equipment
http://www.pilatesinsight.com/pilates-equipment/pilates-chairs.aspx
http://www.pilatesinsight.com/pilates-equipment/pilates-chairs.aspx
http://pilates.about.com/od/buyingequipmentetc/a/Foam-Rollers.htm
The Pilates REFORMER
Most probably the best known Pilates equipment is the Reformer. "With its sophisticated system of springs, straps and pulleys, more than 100 exercises can be performed on this surprisingly versatile apparatus" "The crux is in the gliding platform on which one can sit, kneel, stand or lie on their front, back or side. The user pushes and pulls off the foot bar using the arms, legs, wrists and ankles to slide back and forth along the rails in a controlled manner while the tension in the springs gently works the muscles."
"The
Pilates Reformer helps one establish torso stability and postural alignment while working peripheral limbs in a range of motion. The adjustable springs allow for progressive resistance, which helps to lengthen and strengthen the muscles rather than building bulk. It makes for an effective, no-impact stretching and toning workout that is friendly to the joints."
About STOTT PILATES® Equipment
Q. What is a Reformer?
A. The Reformer is the main piece of equipment used in Pilates exercise. The Reformer glides forward & backward on rollers and uses springs for resistance, along with other attachments, for a wide variety of exercises and positions (i.e. lying down, seated and standing.)
http://www.stottpilates.com/faq.html#anchor_equipment
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| The Pilates Stability CHAIR |
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"Deceptively resembling a stylish little stool, the Pilates Chair (most commonly known as the Wunda Chair or Stability Chair) is one versatile exercise machine. Don't let the word "chair" fool you - it's not necessarily a sit-down work out."
"While many of these Pilates exercises are performed seated on top and pressing down on the step/pedal with your feet, others entail lying on the floor, standing straight up, lunging forward or doing push-up like moves with the arms. More than 75 exercises can be performed on the Chair - it makes it a great addition to your physical fitness routine."
"Once again, adjustable spring resistance is the key to challenge with this specialized piece of fitness equipment. In most models, four springs and five spring attachment positions make for a wide range of resistance. While pressing down on the step with arms or legs, the much of the stabilizing work is up to the torso - it's harder than it looks. This apparatus activates the lower back, buttocks, shoulder, transverses abdominals and pelvic region and heightens neuromuscular coordination. From a rehabilitation perspective, the
Pilates Wunda Chair or
Stability Chair is particularly effective for stretching and re-balancing muscles that have been strained or injured."
"Joseph Pilates' original design had one spring-loaded pedal, but several reputable equipment manufacturers had modified the Chair to expand the exercise potential of the machine. One such modification is splitting the step/pedal so one can work on rotational movement and reciprocal movement of the peripheral limbs. Handles, chair backs, rotational discs and other accessories can be added for increased variety. Some Chairs are designed to be adjustable from high chair to low chair mode."
http://www.pilatesinsight.com/pilates-equipment/pilates-chairs.aspx
The Pilates CADILLAC
"Often referred to as "The Rack" as it resembles something you might find in a medieval torture chamber. But fear not. The Cadillac (also known as the Trapeze Table) is one of the most effective and versatile pieces of exercise equipment ever to be engineered." 
"The Cadillac was originally devised by
Joseph Pilates to rehabilitate bedridden patients back when he was working as a hospital orderly. The apparatus has evolved a bit since the makeshift bed spring days, but its inspiration is apparent and it continues to be a bridge between exercise and physical therapy."
"
The Cadillac is essentially a raised horizontal table-top surrounded by a four-poster frame on which various bars, straps, springs and levers are fixed. Standard models include a push-through bar (which can be sprung from above or below), a roll-down bar, a trapeze or cross bar, arm springs, leg springs, thigh and ankle cuffs and even fuzzy hanging loops. As with most
Pilates equipment pieces, the
Cadillac contains various adjustable parts and you really need a trained instructor to guide you through safe, proper usage and effective technique."
"Over 80 different exercises can be performed on this piece of
Pilates equipment, ranging from gentle spring-assisted sit ups to advanced acrobatics that have one hanging from the upper bars - there's something for all ages and abilities.
The Cadillac repertoire of exercises truly challenges the core abdominal muscles, develops spinal flexibility, works the shoulder girdle, strengthens the back and stretches the total body."
The Pilates FOAM ROLLER
My choice of Pilates Equipment for my own personal home studio is the simple Foam Roller
"Foam rollers are cross-over equipment from rehab training. They are inexpensive, lightweight and versatile -- making them ideal for a home workout or studio. Very simple pieces of equipment (nothing more than a cylinder made of high-density foam) foam rollers are put to all kinds of uses, such as stretching, self-massage, body support, and stability exercises."
http://pilates.about.com/od/buyingequipmentetc/a/Foam-Rollers.htm
Personally at home I do all of the same exercises I teach in my mat classes balancing on my foam Roller. Besides it adding an extra benefit to use my core to stay balanced and stable throughout my workout, it also adds the extra benefit of a spine massage with every workout and is a tool to keep my spine aligned indefinitely.
as a Massage tool:
"Massage Tool: Don't you love it when a massage actually gets to just the spot you need to release? Well, try rolling that muscle or area on the foam roller. Notice I said "on the roller," not "with the roller." That means you actually put your body weight on the roller and gently rock and roll your way to stress relief."
Most probably the best known Pilates equipment is the Reformer. "With its sophisticated system of springs, straps and pulleys, more than 100 exercises can be performed on this surprisingly versatile apparatus"
"Deceptively resembling a stylish little stool, the Pilates Chair (most commonly known as the Wunda Chair or Stability Chair) is one versatile exercise machine. Don't let the word "chair" fool you - it's not necessarily a sit-down work out." 
"Once again, adjustable spring resistance is the key to challenge with this specialized piece of fitness equipment. In most models, four springs and five spring attachment positions make for a wide range of resistance. While pressing down on the step with arms or legs, the much of the stabilizing work is up to the torso - it's harder than it looks. This apparatus activates the lower back, buttocks, shoulder, transverses abdominals and pelvic region and heightens neuromuscular coordination. From a rehabilitation perspective, the Pilates Wunda Chair or Stability Chair is particularly effective for stretching and re-balancing muscles that have been strained or injured."
"The Cadillac was originally devised by Joseph Pilates to rehabilitate bedridden patients back when he was working as a hospital orderly. The apparatus has evolved a bit since the makeshift bed spring days, but its inspiration is apparent and it continues to be a bridge between exercise and physical therapy."
"Over 80 different exercises can be performed on this piece of Pilates equipment, ranging from gentle spring-assisted sit ups to advanced acrobatics that have one hanging from the upper bars - there's something for all ages and abilities. The Cadillac repertoire of exercises truly challenges the core abdominal muscles, develops spinal flexibility, works the shoulder girdle, strengthens the back and stretches the total body."
"Body Part Prop: Under the knees! Lie on your back in rest position and let the foam roller support your slightly bent knees. This position will help lengthen and relax your spine. There are lots of other ways to use the foam rollers as props, but that is my favorite. Other places you might see a foam roller used as a body prop are under the hips or to support a limb."
"Pilates is famous for taking advantage of the core strengthening potential of an unstable surface. As a person tries to maintain balance while working with an unstable surface, all of the deep muscles of the back and abdomen are recruited to help maintain balance. Pilates instructors are inventing many ways to enhance mat exercises and mimic equipment exercises with the foam rollers. Some you might try are exercises like plank or push-up done with your hands on the foam roller instead of the floor" 
