Air sealing materials comprise 1) caulks and foams for small and medium gaps but also 2) weather-stripping materials for windows and doors joints and 3) air barriers (plywood, drywall, rigid foams, housewraps) for large openings and surfaces.
Caulks are intended for small gaps and joints, up to 1/4''/5 mm wide.
Caulks vary a lot in their quality and in their properties and grades - exterior/interior, fire-resistant, high-temp... - which can make the choice tricky, all the more that quality varies between brands and even within the same brand.
See, for details: Caulking Products and their application
Weatherstripping sealing materials
Gaps between the moving parts of doors and windows require specific air-sealing materials: weatherstripping products, namely V-strip seals, gaskets, door bottoms, thresholds, sweeps, etc.
Caulks are used for openings up to, say, 1/4″(about 7mm) in size; for wider openings, use liquid foams.
Most foams are polyurethane-based, but they differ in their properties. Namely, you should distinguish between high-expanding polyurethane and non-expanding polyurethane foams.
Expanding-polyurethane foams come in two varieties (one- and two-part foams) and are for irregular cracks and rough surfaces.
These foams bond well to almost everything, and once you start foaming you shouldn't stop until the can is empty or you are done.
One-part foam canisters are inexpensive ($5-$10 each) and expands a lot; when applying it, you shouldn't fill the whole crack; fill only part of it, and wait for the foam to expand.
Two-part foams are intended for large openings, and to be sprayed onto surfaces. They can also be good insulators, and come with applicator nozzles. They are more expensive (kits: more than $100) and are intended for large projects.
Be aware. Always wear gloves, protective glasses and proper clothing; it will be painful if the foam sticks to any part of your body. Pay attention to the package instructions.
Air Barriers versus Vapor barriers
Vapor barriers (VB) and air barriers (AB) should not be confused. Air barriers are primarily designed to restrict the flow of air, while vapor barriers are specifically designed to restrict the flow of water vapor... A VB does not have to be continuous or free of holes, or to be sealed. An air barrier should be continuous, free of holes and sealed. VB can be important in exterior walls, in regions with freezing temperatures. They are designed to control water and vapor transmission, and to prevent condensation and moisture. Some materials are both air barriers and vapor barriers (retarders), as it is the case of some housewraps. Foams are excellent for sealing holes and cracks around the exterior side of windows and doors, or exposed to sun and moisture.
For deep gaps consider the use of a backer rod (closed-cell material, typically sold in long coils, 1/4 to 1 inch diameter: 7-25mm). Backer rods provide the ideal backing for sealing.
To seal around chimneys or flue pipes use metal flashing, non-combustible materials and fire-rated foams.
Rigid Air sealing materials
Plywood, drywall, polyethylene and housewraps and rigid foam insulation materials like polystyrene are used to air seal large surfaces and very large penetrations, namely in attics and basements. They should provide the continuous air barrier that wood and steel-frame homes should have over their exterior walls, ceilings and foundations...
Image at left (DOE): Home's envelope: orange-red line.
Typical air barriers
Rigid foam boards are great for basement sealing.
Polyethylene sheets are also excellent air barriers, very common in basements. A continuous polyethylene air barrier can make a wood-framed home extremely air-tight.
Many air barriers are available in wide sheets that should be protected from sunlight. To be effective, seal their seams and joints.
More about air barriers:
Air sealing and moisture
See also: OSB, plywood
Housewraps are excellent air barriers in wood- and steel-frame construction. They are typically made from fibrous spun polyolefin plastic, matted into sheets, and are mostly used in new construction (wrapped around the exterior walls, ceiling, floor, foundations...).
To make them stronger, some manufacturers incorporate woven or bonded materials in their housewraps, while others incorporate water-repelling materials.
In hot-humid climate zones, use an housewrap with a water vapor diffusion retarder - often a polyethylene plastic sheet, a foam insulation board or some specific sheathing material... In rainy and wet climates, install felt paper over the housewrap, or use heavy asphalt impregnated building paper...