INVENTIONS
As an inventor, obviously, one of the most noteworthy things about Bill is the fact that he has an entire list of inventions that have in one way or another affected trainers on a daily basis.
The Storage and Retrieval System
Canon: All except the anime
The one invention most people think of when they think of Bill -- both in canon and in the fandom itself. Ironically, it wasn't just his invention. It was actually a joint effort between Bill and the administrator of Hoenn, Lanette, particularly in the reboot of the series. (Read: Gen III started a movement towards retconning certain parts of Bill's past. One of these involved the idea that he was the only developer of the Storage and Retrieval System, and another involved the fact that it was originally a text-based system. As of FRLG, it had a graphical interface, credited as being Lanette's design.)
The technology involved with the system has never really been fully detailed, but its use is straightforward. In order to impose the six-Pokémon limit set by the League, trainers need to have a place to store their Pokémon. From a PC in any Pokémon Center, trainers can access a system that allows them to store their captures digitally as well as rearrange, release, equip, or withdraw the ones already in storage. Additionally, the system is linked to the trainer's Poké Balls, which enables trainers to send Pokémon to storage automatically once their teams reach the six-member limit.
There are a few slight differences in the Storage and Retrieval System in various media. Specifically, in Special, it's known as the Transfer System, the Transfer Storage System, or the Storage System (apparently depending on which panel you're looking at). It's also not entirely clear how one uses the system. In some cases, like with Crystal and Red, it's initially shown that trainers need to have a send point, or a contact on the other end to receive or send their Pokémon whenever they want to deposit or withdraw them. (In other words, it relies on the Teleporter, not on a PC-based system.) However, in other cases like with Red during the Yellow arc and as implied in the GSC arcs, the system works the same way as the games.
Moreover, in Special, there is also a portable version that links to one's Poké Gear. However, only one of these was made, and it was given to Crystal to use due to the fact that the main system was disabled for the entirety of the GSC chapters.
Within the anime, the system is known as the Transport System, and it was actually invented by Professor Akihabara, not Bill. For the most part, it works the same way as the original system in Special, wherein trainers send their Pokémon to a caretaker -- usually the same person who gave the trainer a Pokédex. (For example, Ash sends his Pokémon to Professor Oak, who houses them on a preserve near his laboratory.) Usually, a trainer would have to go to a Pokémon Center and call this caretaker in order to exchange Pokémon (via a machine near the video phones), although the anime attempted to set up a system in which exchanges could happen via the Pokédex itself.
In all other incarnations, Bill is the sole inventor, and it works the same way as the games.
The Teleporter
Canon: All except the anime
The other invention most people think of when they think of Bill. As a vital part of his research in digital transportation, Bill has developed a device that allows objects to be transported instantly from one point to another. Although it serves as a basis for the Storage and Retrieval System (especially in Special), it doesn't seem to serve any other purpose except to be a reference to The Fly.
Bill's notorious accident with it has also driven him to develop a side program for it meant to divide DNA codes within organisms that happened to be multiple species merged together. This is called the Cell Separation System and also serves no actual purpose for trainers. Rather, it was added exclusively to bring Bill's mini-storyline to a significantly happier ending than the movie it's referencing.
The Time Capsule
Canon: GSC
GSC presented a rather unique problem to the game developers: compatibility issues. Namely, they wanted players to be able to trade between Gen I and Gen II, but they couldn't due to the fact that the games introduced a lot of new features (read: Pokémon and moves) that literally didn't exist in Gen I. The answer was to dust off Bill's character and give him something else to do.
The end result was the Time Capsule, essentially a time machine located in the upper floors of any Pokémon Center. If a trainer met all of the requirements (met Bill in Ecruteak City, waited a day, and had a team that contained no Gen II Pokémon or Pokémon with Gen II moves), they could use the Time Capsule to send their Pokémon back in time to trade with a trainer from three years in the past (i.e., playing a Gen I game). How this works seems to differ from official art and the game itself. Sugimori art shows a trainer standing in front of the Time Capsule (a tube-like device) with a Poké Ball in it, implying that the trainer didn't actually have to be face-to-face with his or her partner to trade. However, in the game, it shows the trainer actually entering a room (presumably by going back in time via the capsule) to trade face-to-face with a Kanto trainer.
Either way, because the issue was answered in HGSS with the Pal Park, this was one of the inventions altered due to the retcons starting in Gen III. As a result, this technically never existed in the updated version of Bill's backstory. Which is a shame because this would mean Bill invented a time machine and because the fact that this doesn't exist causes his dialogue in HGSS's Ecruteak City to be rather random. (In HGSS's Ecruteak encounter, he stops you to talk about the storage system and Lanette. Why? ...Good question.)
The VS Seeker
Canon: Special
In Special only, Bill developed a small, portable device that detected the presence of trainers within a certain number of feet. It apparently operates by sensing the "hostile signals" emitted by trainers. (In other words, one might say that it's actually a psychic device, but as usual for the franchise, the specific technology is rather vague.) As a further note, this is the only canon where it's stated that Bill developed the VS Seeker; in all others, the actual inventor is never given.