I hear a lot of people mentioning that they use little apart from clay and paint when making sculpture. I think some people are a little intimidated by the range of mediums, chemicals, sprays and such that are on the market. It is easy to become overwhelmed, but with a bit of background knowledge they can only help your work.
I'm a huge fan of all these liquids, I use them all on different sculptures, and you don't only need to use them as the label states! Go ahead and cook up dozens of little sample pieces of clay and apply various mediums and combinations onto them to see the effects you can get.

Disclaimer:
Many of these chemicals are carcinogens, and none are good to breathe in. Always read the labels and follow the safety guidelines. Especially with sprays and fuming chemicals you need to be sure to wear a mask. Wear gloves too (a kind that wont be dissolved by the chemical you're using.)
Work outside when possible, or at least have a fan or two running with a window or door open. Here we go!

1: SPRAYS

A: Clear Spray.
I use this spray when I'm using pastels to colour a sculpture. You can find information online on this technique, but it involves applying spray, then pastel dust, then spray- over and over, gradually building up the colour. A sculpture done this way can have dozens and dozens, perhaps hundreds of layers of spray!
B: Spray Adhesive
Usually I use this for sticking sheets of armature blueprints into a sketchbook for reference. I also used it for the armature of my taxidermy unicorn, to stick many layers of cardboard together.
C: Polyurethane
I sometimes use this in place of binder medium, to seal the porous surface. I sometimes use it as a glaze too, and for woodwork, of course. It is especially good to use if you've made a sculpture or object out of a porous clay and wish to cast it, as a few layers will smooth out the surface.
D: Fixative
Most people are familiar with fixative, I use it mainly for drawings and painting, but it can also be used on sculptures.

2: GOOD OLD FASHIONED CHEMICALS

A: is for Acetone
I love acetone. I really do, I have used it for years and can't imagine life without it. I use it for everything- cleaning dried paint from brushes, dissolving glues, etc. Acetone basically attacks plastics and breaks them down. Its effects depend heavily on the type of plastics. Some will instantly dissolve completely, others (like PVC) dissolve more slowly. It is carcinogenic so don't get it on your skin! It should be put in a metal or glass container to work with, and it evaporates fast, within a few minutes. I usually keep it in a glass spice jar with a lid on. One of the best things it will do is dissolve cured polymer clay very gently, so if you get a sculpture out of the oven and it has a crack, simply wet a brush with acetone and work it into the area in circular motions. It will dissolve a small amount of surface clay which will get driven into the crack, filling it. It will then simply evaporate off of the sculpture. Good stuff.
B: Mineral Spirits
You can use turpentine, turpenoid, and mineral spirits in the same way. Use it on an uncured polymer clay sculpture in the same way you'd use slip on a stoneware piece. It will smooth out areas and get rid of fingerprints and such. It's best to use it at the very end as a final touch. Leave it a day before baking to allow the spirits to evaporate completely. Don't overuse it, it will happily turn your sculpture into a mash you are unable to work with for days until it evaporates.
C: Lacquer Thinner
This is nasty stuff. The fumes will knock you out, so wear a mask when possible. I use this to clean the tiny metal parts of my airbrush, and to clean things acetone won't clean. It is like a more hardcore version of acetone in a lot of ways, so use it scarcely and minimally, and don't spill it on your desk because as the title implies, it will thin your lacquer.

3: CASTING MATERIAL

I use this to make eyes mainly. The stuff in the blue can is resin, and will harden once the activator (little bottle in front you can only see the lid of) is added. If done right, it will become like glass, and can take the heat used to bake polymer clay. The stuff on top is a two-part epoxy resin. The dark blue bottle in front is a release agent. Apply it to your mold minimally to allow for easy removal of the cast.

4: GLUES

A: White Glue
We've all used this, I use it for papier mache work mainly, but also for sticking card together and watering down to use as a shiny glaze.
B: Fabri-Tac
I get LOADS of questions about how I attach hair, and Fabri-Tac is the answer to all of them. Don't be tempted to go with a cheaper glue that does the same thing, they don't! Also go with smaller bottles as it tends to harden over months (weeks if you lose the lid.) The money you save by buying in bulk is outweighed by the wastage you'll get if you buy big bottles.
C: Non-porous glue
This is not brand-specific, you can buy any kind of non-porous glue. It's usually used to attach metal wire and beads to stuff, but it will also bind clay. If you coat your entire armature in it, for instance, it will bind the clay to it as well as floral tape. It is especially useful for wing armatures where you use aluminium sheeting or mesh for the armature, and it is too shapely for floral tape. It will be fine in the oven.
D: Craft Glue
Good for general purpose things like paperwork, sticking fabrics together, etc.

5: GOLDEN MEDIUMS

A:Soft Gel (semi-gloss)
B: Soft Gel (gloss)
D: High Solid Gel
These are all used for the same thing- building things up. For example you can use it to make a mermaid tail by making the tail shape from tissue and then applying the gel over it- it will take a day to dry but when it does so it will dry to a crystal clear finish. Use for things like fairy wings too.
C: Gesso
This is my tiny jar of gesso. I have a 2 gallon bucket in my painting studio! It's used to prime surfaces for oil painting, but you can apply it to a sculpture on which you're going to use the pasteling technique. You can apply gesso to just about everything and once dry it is an instant painting surface for any medium.

6: PAINTING MEDIUMS

A: Dammas Varnish
This is half my collection of mediums, the rest is in my painting studio! Dammar varnish mixed with liquin, linseed oil and turpentine will create a lush glaze that you can use on a painting, it will make the colours luminous and permanently liquid-looking.
B: Masking fluid
I use this mainly for covering glass eyes when using the pastel technique, so they're not coated in a hundred layers of spray and pastels. after you're done you simply peel the rubbery layer off and the protected object is there, perfectly clean. You can use it to great effect in watercolour painting too.
C: Same thing as B, opps!
D: Linseed oil
A good medium for oils that makes them a little glaze-y and (when you get the drying type here) helps the drying time.
E: Liquin
This is good for adding to oils to make them dry really fast and, like linseed, making them good for fine detail work. Unlike linseed though it will not make much of a gloss.

7: LEAFING LIQUIDS

One primes the surface for the leaf, you can apply it to a very specific area, apply the metal leaf, then rub it away and it will only apply to the primed area. The other is a medium that will seal it.

8: LIQUITEX MEDIUMS

A: Modeling Paste
This is good stuff! Think of it as liquid clay, you can apply it to a cured sculpture with a brush t create things like veins and filling cracks. It will dry to an off-white solid and can be sanded.
B: Flow Aid
This can be mixed with acrylics to allow fine detail work, it's like the liquin of acrylics.
C: Glazing medium
Good for mixing with acrylics when you want to create a bit of a gloss!
D: Glaze medium and Varnish
Glaze varnish is good for applying to part of a sculpture you want glossy, but not too glossy. Sculpey gloss glaze and clear enamel will make what they're applied to REALLY shiny, and if you're glossing something like nostrils, around eyes, beaks, or claws you only need a soft gloss.
E: Retarder
This will slow down the drying time of acrylics by a few minutes. And if you've use acrylics you know how valuable a few minutes can be!

9: FIBERGLASS RESIN

I LOVE fiberglass! Shown is only the resin, I have the fiberglass in my drawer. It is what the enormous sculptural objects and facades you see in themeparks are made from, and many people make sculptures with it. I've only used it for repair work so far (hot tub shell, lawnmower engine, etc,) but I am going to make a sculpture with it after graduation. Make sure whatever you're wearing is fully disposable!

10: ATELIER AND GOLDEN MEDIUMS

A: Matte Medium and Varnish
This is what 95% of my sculptures are finished with. It seals everything below and allows for cleaning of the work. The matte is a very nice natural type, good for everything!
B: Fast Medium
Acrylic is deceitful. After 10 minutes most people would call it dry, but in reality it takes a few days to fully dry. This medium will speed that complete drying period to under and hour, it is perfect if you're planning to do oil-like glazing techniques with acrylic.
C: Binder Medium
This is what I apply directly over all my polymer clay sculptures. It seals the porous surface and, like gesso, will allow you to paint it without it flaking or peeling.
D: Acrylic Flow Release
Use this to water down acrylic in place of water. Using water simply dilutes the paint and then leaves the molecules haphazardly spread as it evaporates, but as flow release is an acrylic-based medium, it will hold the paint within it and dry along with it, creating a more substantial layer.
E: GAC 400
this is a fabric stiffener. Apply it to any natural fabric (like cotton or linen) and it will stiffen and become hard. Using it you can essentially make sculptures from cloth! But I use it mainly within a sculpture. There is an orange Kirin in my gallery who has fins and a fin-like tail, I used this medium to harden those.

11: RANDOM
Mineral oil is good for smoothing out areas of a sculpture like mineral spirits, but unlike mineral spirits it rolls over the surface instead of actually breaking down small amounts of clay. It can be deceptively awesome, but overuse it and the sculpt will become an unworkable mass- but unlike with turpentine, it will NOT evaporate! It will sit there and need to be leeched out with tissue and paper over days, very hard work. Also if you use too much it will cause cracking in the sculpture when baked.
Aspirin is for when you've been sculpting too much.

12: POLYMER CLAY SPECIFIC MEDIUMS

A: Sculpey clay softener
This is essentially plasticizer, add it to clays you find too hard or old and dry to work with, but if overused it will have the same effect as mineral oil, and will have to be leeched out of the clay. In small amounts it's very useful.
B: TLS- translucent liquid sculpey
TLS is sort of like glue for polymer clay. If you need to attach two pieces of clay (uncured to uncured or uncured to cured,) then score the area(s) to be attached and then apply TLS and press them together. It's the same way you'd attach a handle to a mug with stoneware throwing.
C: Fimo Gel
This can be tricky to get hold of, but it's worth it! TLS will boast that it cures to a clear finish, but it bakes to be milky. Fimo gel on the other hand will bake to a crystal clear finish, and can be used for things like making eyes, wings, fins, etc. Many fairy wings you'll see on dolls are made using this baked between wire armatures.