VEX offers a large variety of parts to use, and the fact that most parts can be modified allows for a wide variety of building techniques and possible designs. However, certain parts not available on the VEX store but still are competition legal can further increase possibilities and help take your team to the next level, whatever that may be for you.
Legal Plastics
Robot rule 7 states that "polycarbonate (Lexan), acetel monopolymer (Delrin), acetal copolymer (Acetron GP), POM (acetal), ABS, PEEK, PET, HDPE, LDPE, Nylon (all grades), Polypropylene, FEP; as cut from a single 12” x 24” sheet up to 0.070” thick" may be used, and that "Plastic may be mechanically altered by cutting, drilling, bending etc. It cannot be chemically treated, melted, or cast. Heating polycarbonate to aid in bending is acceptable." For newer competitors, the importance of this may be hard to understand, but there are many many things that can be done with plastics. The most common type used in VEX is polycarbonate, and it is typically used for very low stress structure such as flywheel hoods (which also benefit from the flexible nature of polycarbonate which allows easy curves to be made), and to cover space to prevent game objects from falling through (and also to put stickers on but shhh). I personally do not have experience with other types of plastics, but I'm certain they have a use for some niche mechanism.
Anti-slip (grip/friction) Mat
This product goes by many names but is essentially a net of small rubber feet. As the name would imply, this stops things from sliding around, so it is good for intakes that clamp down on game objects so they don't fall out. However, anti-slip mat can also be used as a net to hold game objects loosely, like 185A from Starstruck.
Rubber bands
Vex does sell rubber bands, but the importance of having quality rubber bands cannot be undersold. Fishing rubber bands are good for this purpose, but make sure they are of a legal size (#32 or #64).
Zip ties
Vex also sells these, but they have uses beyond securing cables. They are perfect for attaching rubber bands to c-channels, and also can help mount license plates in easier to reach spots.
Thin nylocks
These parts are available on robosource.com, and they are essentially a strict upgrade to the VEX nylocks, as they weigh significantly less than but provide the same security as the VEX nylocks. The lower profile they have also helps in building lifts, as space sometimes gets to be tight.
Nylon screws/nuts
The weight of all the screws on a robot may not seem signifcant, but it adds up over time. Nylon screws, though not very strong under load, are perfect for securing bearings if well tightened and can reduce your robots weight by a few tenths of a percent if used for all bearings.
11/32 in socket wrench (nut driver)