I have actually had many, many different fan game ideas (none of which, predictably, have come to fruition thus far), and this topic greatly intrigues me.
I guess I'll start with my most notable ones, though.
IDEA 01: Touhou Card Game
Yes, yes, I too have dreamed up a card game. The principal behind was rather simple - you choose three characters out of your Deck at the beginning of the game to represent you. Those three are essentially your girls for the entire duel, as you do not bring out new girls later or anything like that. Rather, after you have selected your three players, other characters that you may have in your Deck may offer their assistances in the form of abilities and boons; think SA, with Yukari for example giving a Border-Bending ability to one of your three playable characters.
Primary stats for the playables would be HP, SHOT, DODGE, and SPEED. Your girls' powers and abilities would be enhanced through assist characters from your hand, Generic Danmaku Attack Cards, and character-specific Spell Cards. There would also be Incident Cards that trigger effects on the game as a whole.
The obvious goal here is to eliminate all the lives of your opponent's team (different characters would have different amounts of Lives and HP), while keeping your own girls alive. Important factors for success would be building your Deck around the characters you use most frequently (for example, don't bother including cards specifically for Yukari if all you ever use her for is as an Assist), as well making sure to pick a well-balanced trio, one with lots of synergy and who are able to cover each other's weaknesses. If you pick three powerhouses that all have low HP, you won't get very far.
I have a concept draft of the rules, but it isn't finalized. I DO have a finalized design for the cards though. I will share when I have access to my broken computer (haha).
IDEA 02: Touhou Chess
Now this is a very fun idea here, and me and a friend of mine have already drafted the entirety of the rules. Touhou Chess is basically chess, but with some added rules. First of all, your specific Chess Team is decided before the game starts - there is one team from each main game in the series, as well as a couple extra teams to fill in the blanks.
The primary principal of Touhou Chess is that every time a piece is captured, both players score SP, although the capturing player scores more. During a player's turn, they can forgo their standard move in order to cast a Spell Attack - this can be a Generic Spell which all teams have access to, or a Specific Spell, which only the character in question would have access to.
Here's an example.
The Generic Spell "Forward Barrage" is an attack which any Rook character can use, regardless of team. It allows that Rook to select any piece that is within its striking range and take it out, without actually having to move from its spot.
Meanwhile, Yuyuko's "Resurrection Butterfly" is a Spell which only she can use, and is thus restricted to the PCB Team (where Yuyuko is the King Piece). It allows her to once per game, after it has been cast, evade one Checkmate by moving to the nearest Safe Space. Spells will cast varying amounts of SP to cast depending on how powerful/advantageous they are.
Another aspect is the Team Ability - every team has a semi-unique ability (each ability is shared by only two teams) which is always active. For example, the LLS Team has an ability which allows them to score double SP whenever one of their own pieces is Captured, allowing them to fire off Spells in quick succession (on the other hand, that team has a lot of expensive spells).
Like I said, the rules and Spells are already set and written (with minor testing still needing to be done to ensure balance). This game simply needs to actually get programmed - I would need Sprites, Portraits, and most importantly, coding for a large, 3D (with 2D sprites) Chess environment, as well as the coding to implement the various Abilities and Spell Attacks.
IDEA 03: Various Danmaku games
These, I am actually having more luck getting off the ground. I essentially have three in the works: one where you choose from several teams of three to play through the storyline (and between the combination of all the playable teams, every Windows character pre-TD makes an appearance, as well as some additional characters), one that features a full cast of new characters to fight against while playing as series regulars (so the closest thing to an actual new Touhou game), and a Phantasmagoria title featuring canon characters as well as 4 OCs.
Between the three, I have the most development on the second one. In fact, here's a proof of concept:
And that's it for me!