Is it possible to trade Pokemon from the 1st generation games to the most recent ones?

You cannot trade from the 1st Generation or 2nd Generation into the 3rd Generation and onwards.

While it may not be possible to transfer from Gens I and II to III, seeing as Gen III has FireRed and LeafGreen, it would be advisable to just play through that and trade upwards (to gens IV and V) from there..

Yes, you can trade from Generation 1 and 2 cartridges (not just Virtual Console) to more recent generations

However, it is not something that is officially supported by Nintendo.

The website Atop the Fourth Wall posted a how-to video showing that it was absolutely possible to go from Generation 1 and 2 cartridge all the way to Generation 6, the latest as of the video's creation. Since it ends with the Pokémon Bank, you can presumably go to any generation after that.

A tutorial on trading up Pokémon off of Generation 1 and 2 cartridges and into the modern generations! Yes, it IS possible.

It does involve using hardware to extract your save file from the cartridge and manipulating it using a save game editor. Still, the end result is having your original team from a Generation 1 or 2 cartridge transferrable all the way to the Pokébank.

This is technically possible now that the Gen 1 Vurtual Console games support migration to Sun and Moon.

It's not easy and is only doable with pricey hardware.

The steps are as follows:

1. Dump your save game from your original Pokemon Red, Blue or Yellow cartridge to your PC using either a Retron 5, Retro Freak, or some other Game Boy cartridge reader. You can build one with an Arduino if you're good at soldering and don't mind destroying a Game Boy for the cartridge slot. Depending on the hardware you choose this step will be expensive or time consuming.

2. Hack your 3DS so that it can run homebrew. I won't go into the steps for this because it's against Nintendo's terms of service but on the latest firmware it requires you to buy a game that has an exploitable defect. This will cost you due to the popularity and rarity of those games.

3. Purchase and download the Virtual Console version of the same Pokemon game that you copied the save from and start a new game.

4. Use homebrew software such as SaveDataFiler to replace the Virtual Console game's save file with the one you dumped earlier from your original cartridge.

5. You now have a working copy of your original game's save file on your 3DS. Use Pokemon Bank to migrate your original team to Pokemon Sun and Moon.

• Generation 1 (Red/Blue/Green/Yellow)
  ?? Both directions
• Generation 2 (Gold/Silver/Crystal)
  X Trade impossible
• Generation 3 (Ruby/Sapphire/Emerald/FireRed/LeafGreen)
  ? One-way only
• Generation 4 (Diamond/Pearl/Platinum/HeartGold/SoulSilver)
  ? One-way only, no items
• Generation 5 (Black (2)/White (2))
  X Trade impossible*
• Generation 6 (XY/ORAS)

*It is not possible to trade pokémon from Generation 5 to Generation 6. As explained on the official website:

There are a number of differences between the functions and specifications of the Nintendo 3DS family of systems compared to other systems in the Nintendo DS family (DSi XL/DSi/DS Lite/DS), meaning that it is unfortunately not possible to communicate directly between software made for the two different systems (models).

However, a paid service called Pokémon Bank has been created to fulfil this gap. The service costs $4.99 (yearly subscription) and it allows users to upload their pokémon to the cloud. The "uploading" service can be used on both 5th and 6th generations, while the "downloading" service can only be used on Pokémon X and Y. Using this service allows de facto the users to trade pokémon from generation 3 up to 6.