There are quite a few chemicals available which can be added to the motor oil/crankcase for various purposes.
Repair Chemicals
Some chemicals are designed to fix problems which would be costly/time consuming to fix conventionally. A popular type is leak sealer, but there are also options like compression repair (Rislone's product is shown at the right) and rear main seal repair.
High Mileage Chemicals
Chemicals deisnged to help high mileage engines are very similar to repair chemicals, but are more directed at preventing problems before they occur. Some of these chemicals are already added in to high mileage formula motor oil, but which chemicals are used differ from brand to brand, and will need to comply with the API certification printed on the bottle.
Break-In Oil
Break-in oil, like the example bottle on the left, is designed to help new engines deal with the stresses of new components encountering friction for the first time. It often contains extra zinc, and only needs to be in the crankcase until the first oil change. After the engine is broken in, break-in oil can still be used, but won't have too much of an effect, and may reduce oil life or damage the catalytic converter.
Zinc & Phosphorus
Zinc additives are good for sealing up cracks in metal within the engine, and helps with cold starts where oil may not be ready in the engine due to the zinc being already stuck to the friction surfaces. It is also a preferred additive for breaking in new engines, especially ones intended for motorsport use. It is also added from time to time by vehicle owners that go the extra mile to take care of their engine.
ZDDP (which stands for Zinc Dialkyldithiophosphate) Zinc and Phosphorus EP (extreme pressure) additives help protect internal engine components including pistons, flat tappet style camshafts, valve lifters, pushrod tips and the valvetrain in general. These additives are most helpful in high-performance situations/applications, but all engines can benefit from them.
Seal Repair
Some chemicals can treat rubber seals which are found in a number of locations in the engine, such as where the crankshaft meets the engine block. The chemicals are designed to keep the seals from decaying with age, to help them resist being broken down by hot oil, and sometimes to soften or swell the seals. The chemicals include polymers, lubricity agents, anti-oxidants, and conditioners.
If you are installing seals and have a seal repair oil additive on hand, it is better to coat the surfaces with it than with the basic motor oil, since it will help form a better seal.
Rear Main Seal Repair
Some products are designed specifically for the rear main seal, which is one of the most stressed seals in the engine. An example of that product is shown at the left, and is produced by Bar's Leaks. Some rear main seal repair additives are meant to slightly swell the seal, pushing it against the crankshaft in an attempt to get it to seal again. Due to the different ways rear main seals can fail, this approach has varying degrees of succes.
Stabilizers
Oil that doesn't get used for a long time might break down or lose its beneficial lubrication properties. Oil stabilizer can reverse that process, or prevent it from happening.
Some companies have special stabilizer formulations for synthetic oils. Getting the wrong stabilizer won't ruin the oil, since the chemical differences are barely noticable, but it won't be optimal if normal stabilizer is used in synthetic oil.
Do Oil Additives Actually Work?
Some mechanics will tell you some of these chemicals are useless, while others are big fans. What does and doesn't work will always depend on the application, the type of chemical used, and the product's quality. Some types of chemicals need to be high quality, while others work very well even as a low-price store brand.
Most leaks can't be truly sealed with a chemical, but many repair chemical products do quite a good job of reducing the problem until a real repair can be made.
Potential Problems
One potential problem you can have when using these chemicals has nothing to do with the chemical itself, but the amount. Pouring in a bottle of anything adds to the oil level, and if the level is too high, it could slow the engine down (make it work harder) or even damage it. Some companies have started selling their additives in smaller bottles due to people not reading the directions, pouring in the whole bottle, and having problems afterwards.
Recommendations
This site tries to keep all of its articles as unbiased as possible. However, if you would like an actual recommendation from the owner of this site, be sure to check out Steve's Automotive Chemical Recommendations Page. In general, Steve always recommends just repairing a problem instead of using a repair chemical.