I'm familiar with TCG's that employ banned or restricted lists for cards that are deemed to powerful for fun, interactive gameplay. Are there any other types of games that have similar ways of affecting game balance after release? Is this a feature present in other games with expansions? Are there any games without expansions that have had game balancing bans/restrictions created by the game maker or game community?
Miniatures games often have units or models banned if they are over powered or "break" the game. Generally it's less frequent than w/ some CCGs, but it does happen. That said bannings are often specific to a specific tournament rules set (LVO vs ITC for 40k) rather than issued by the creators of the game, especially when the game creators don't actively support tournaments. On the other hand most miniatures companies that do support tournaments tend towards errata rather than outright bans (See X-Wing Miniatures from FFG).
Expandable Card Games (a.k.a. Living Card Games®) also do it. These are pretty much just like Trading Card Games, but instead of buying booster packs of random cards, you can buy a set that contains multiple copies of all the cards in the set. Fantasy Flight Games popularized this under their registered trademark Living Card Games®.
A Game of Thrones is one such game that has banned cards. For instance, their 2010 tournament rules noted that in the standard LCG format, the cards "Pyromancer's Cache", "Jaqen H'Ghar", and "Compelled by the Rock" were all banned (although some of these were later removed from the ban list).
Note that this is not always the case for ECGs. Doomtown Reloaded had several broken cards like "Hot Lead Flyin'", but instead of banning it, they just provided errata that made some radical changes. In many cases, future sets included four copies of a previously errata'ed card so that players could have a card with the corrected text on it.
Banned and Restricted cards and/or pieces only matter in official gameplay matches.
If you are paying with your friends or family for instance there's no need to follow those restrictions anymore than a need to follow any other restriction in a board game. That is to say you follow what you feel is necessary. If, for example, you feel that waiting until your turn to draw a Carcassone tile needlessly elongates everyone's turn then you can do as many people do and draw the file after your turn so you can begin considering placement while you wait.
This of course doesn't mean that all rules are so easily broken to no detriment. We have the infamous case of Monopoly with so many home rules which often do nothing but change the rewards superficially while oftentimes ruining the balance of the game.
Banned and Restricted cards can fall into either of those categories. There are cards which are banned because they unfairly balance the gameplay in high level dedicated play. There are also cards which are restricted for other reasons. Any game with "Official Play" is likely to have those types of Restrictions. The most prominent example being Living Card Games (LCGs) which have official play and may restrict cards which will unbalance the game or cards which are too old for the current meta. They might often release expansion sets in waves or seasons and restrict older season cards as newer seasons are released. From a business standpoint this of course incentives the players to buy the newer sets even if the card abilities they want are already featured in older sets. Evolution rebalanced their cards and now that they have tournament kits they likely restrict those older cards.
In short again any game with official play will be a candidate for Restriction and Banning. It's not impossible in games without official gameplay it's just less likely. I'd be more common to errata the card, or release a new version as a replacement but again with out an official play there's no need or way to ban it.
I can name one such example - Seasons. There is a list of "tournament allowed cards" Thought those cards are perfectly fine in any casual game (and honestly, I don't see much reason behind restriction)
Many games of all types have errata that are published after the game is released, to change the way the game plays or fix balance issues or generally to make the game better. It is quite common in wargames to have "Living Rules" that change over time adding and removing features of the game to address problems that occur either in official tournaments or just to make gameplay smoother.