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

I know that you can trade Pokemon between games of the same generation (Gold/Silver, Ruby/Sapphire) and even trade between 1st gen and 2nd gen. However, I haven't been able to find a way to trade Pokemon so that I can play with my 1st generation Pokemon in HeartGold, for instance. If it is possible, how many steps would it take and what equipment would I need?

As of 2016, it is possible to trade from the Virtual Console editions of Pokémon Red, Blue, Green and Yellow to the new Pokémon Sun/Moon (Gen 7) via Pokémon Bank.

Unfortunately while Gen 6 (X/Y/OR/AS) is compatible with Pokémon Bank, it is not possible to receive Gen 1 Pokémon in those games.

However, if we're talking about the original Gameboy cartridges, it can't be done. The limits on trading are as follows:

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, allows held items
Generation 4 (Diamond/Pearl/Platinum/HeartGold/SoulSilver)
↓ One-way only, no items
Generation 5 (Black/White/Black 2/White 2)
↓ One-way only, no items
Generation 6 (X/Y/Omega Ruby/Alpha Sapphire)
↓? (Unreleased, backwards trading yet to be confirmed, Pokémon Bank currently forbids items)
Generation 7 (Sun/Moon)

There are three main reasons you can't trade between Gen I/II and Gen III:

1. The Pokémon data format changed significantly in Gen III, so the two were incompatible.
2. The GBA link cable uses a different voltage to the Gameboy link cable. Even though a GBA can play old Gameboy games, it uses different circuitry than when playing GBA games, so the games' link cable functionalities are fundamentally incompatible.
3. Even if these weren't an issue, Nintendo never released a product that allowed trade from one to the next.

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..