I've made great games by being inspired by other games. Usually, I saw an idea or mechanic from another game, and thought I could do it better.
I played Istanbul, and I loved the idea of going around a city, with lots of things to do, and a few characters to meet. However, all the player was doing was hauling around gems on a cart, using a kind of retracing-your-steps movement system. I decided to make my own game. It's not about gems on carts, and it has no funny movement system. In my game, you find treasure, fight with other players, acquire and complete quests, and go to all kinds of interesting events and places. Was my game inspired by Istanbul? Yes. Is it similar to Istanbul? Only slightly, in that both games involve moving around a city.
Inspiration from other games is also an excellent safety net. If you can't get things to work, you can always "cheat", by seeing how the original game did it. More importantly, you know there's actually a good game out there in that patch of possibility. I've made games that were extremely novel, but never got them to a stage where they were any good. There was no "original" to copy a mechanic from.
If your game is inspired by another game, it's really inspired by the mechanics of another game. This means you're free to change the theme. You should change the theme to something totally different, if you can. This is a way to make your game seem nothing like the original game. For instance, if the game is futuristic, make yours historical or fantasy. Go even further, if you can.
In the Dungeons and Dragons-themed game Lords of Waterdeep, players place their agents around a city, gathering wizards and warriors, in order to complete quests and get a reward. I also made my own game — Gastronome. In this game, chefs moved around a farm cottage, gathering ingredients, so they could follow recipes, in order to prepare dishes. You can tell from this story that these are the same game, but experienced players of Lords of Waterdeep never made the connection, even when told that Gastronome was a clone of a game they played regularly. Gastronome was just an exercise, however, and I didn't try to publish it.
Almost all games take inspiration from previous games in some way, but
if you want to get published, your end product must be clearly and
significantly different from the original. There isn't a rule against copying, but people regard unoriginal games in low regard.
It's easy to be too inspired by another game, and just end up referring back to it, every time you have to make a design choice. If that's the case, your game is too similar to the original. To avoid this, be inspired by multiple games at once, or add in something fundamentally different. Then, the path your game takes will necessarily be significantly different.
Players' time, comprehension, and money are all limited. You cannot make a game of unlimited scope. You shouldn't just take the game that's inspired you, and add stuff to
it.
You need to decide what your game isn't about. These are things from the original game that will be absent, simplified or merged, in your game. I call this zoom.
Maybe things are very similar, but you're zooming in on something that wasn't central before.
I like the farming game Agricola. It has inspired several of my prototypes. One was zoomed in, where the animals and crops were central, and more complex, but the farm itself was simplified, and other systems were absent. Another prototype was zoomed out, and you were running a whole farming village, with an army, and things you could build. The farming was still present, but it was very much simplified.
In Magic, creature combat is about two numbers — power
and toughness. Combat is a numerical tradeoff puzzle. Some creatures
have abilities that affect the combat, but most don't (some have simple
or ignorable abilities.)
Radlands has people in it, similar to Magic's creatures. However, I
really like abilities and special powers, so the people in my game have
lots of abilities, but I intentionally omitted numerical strength or
life amounts. People in Radlands don't have a power or toughness number
at all.