For the purposes of the answer, "transfer" shall mean moving a Pokemon between games that are unable to communicate via trade.
Summary
In general: You can transfer Pokemon to a game from a later generation or the same generation, but not to a previous generation. For example, Pokemon in Gen 6 can be transferred to Gen 7. However, you cannot transfer from Gen 7 to Gen 6, even if the Pokemon originated from Gen 6. (See Footnote 1 and 2 for exceptions.)
It is also possible to trade Pokemon between copies of the same game (where, for example, Sword and Shield are considered the same game). Until Gen 8 and excepting LGP/E, it is possible to trade Pokemon between main series games of the same generation. For example, Diamond/Pearl and HeartGold/SoulSilver can trade with each other, as both games are in Gen 4. (See Footnote 2 for exceptions.)
Depending on the game you're playing, Pokemon may be transferred to and from Pokemon Home and Pokemon Bank, which are cross-generational storage services (but still bar you from transferring backwards in generations).
Flowchart
Refer to the flowchart below to see where your Pokemon can go. Take note that the arrows are one-way; a Pokemon cannot be transferred against the direction of the arrowhead (and where it can be transferred both ways, a second arrow going the opposite direction is included). Games from the same generation that cannot trade with each other are separated by dashed lines.
Please credit me or PokeBase if you re-use this chart.
* This diagram considers Virtual Console games to belong to their original generations. So, per usual rules, Pokemon in Gen 7 cannot be transferred to Virtual Console games.
** LGP/E is considered to be part of Gen 7, but it has no interactivity with other Gen 7 instalments in the series. Pokemon from LGP/E can go to and from Home, but once they're transferred to Gen 8, they cannot go back to LGP/E.
Footnotes
#1: It is possible to transfer Pokemon from Gen 2 to Gen 1 if the Pokemon is present in Gen 1 and it knows only moves present in Gen 1.
#2: The Pokemon (and its held item, where this can be traded/transferred) must exist in the destination game for this to work. For example, Poipole and Naganadel cannot be traded to Sun/Moon from Ultra Sun/Ultra Moon. Further, Incineroar cannot be transferred into BD/SP. Also, via Pokemon Home, all transferred Pokemon will have their learned moves "reset" based upon their level-up movepool in the destination game. See here for additional restrictions to Pokemon Home and here for restrictions to Pokemon Bank.
