I'm planning on taking on this community challenge. However, before my tics get tactical, I'd appreciate some feedback on he simpler implementation.

Factoring in all the logic/edge conditionals was unexpectedly challenging and leaves me wondering if:

1. This is done efficiently? Get the feeling that some of this is done in a roundabout way.
2. Does it break any conventions?
3. How are the variable and method names? I always particularly welcome suggestions on this names are hard.
4. A few of my variables are static, I'd like to know if any are when they don't necessarily have to/shouldn't be.
5. The location of variables. I know this can be opinion based, but I always have several in mind and I can't know which is more understandable to someone else.

I'm planning on refactoring most of the main class as a board class for the challenge, so only take this in terms of Tic-Tac-Toe.

###TicTacToeSquare

import javafx.scene.control.Button;

public class TicTacToeSquare {
    private boolean filled;
    static boolean turnTracker;
    private Button square = new Button();
    private final int SQUARE_SIZE = 100;

    TicTacToeSquare() {
        square.setMinHeight(SQUARE_SIZE);
        square.setMinWidth(SQUARE_SIZE);
        square.setOnAction(e -> {
            if (square.getText().isEmpty()) {
                square.setText(turnTracker ? "O" : "X");
                square.setStyle(
                    turnTracker ? "-fx-text-fill: gold;" : "-fx-text-fill: darkred;");
                filled = true;
                turnTracker = turnTracker ? false : true;
                TicTacToe.evaluateBoard();
            }
        });
    }

    public Button button() {
        return square;
    }

    public boolean equals(TicTacToeSquare target) {
        return filled && square.getText().equals(target.button().getText());
    }

    public void clear() {
        filled = false;
        square.setText("");
        square.setDisable(false);
    }
}

##TicTacToe

import javafx.application.Application;
import javafx.application.Platform;
import javafx.geometry.Insets;
import javafx.geometry.Pos;
import javafx.beans.binding.Bindings;
import javafx.beans.property.IntegerProperty;
import javafx.beans.property.SimpleIntegerProperty;
import javafx.beans.property.StringProperty;
import javafx.beans.property.SimpleStringProperty;
import javafx.scene.Scene;
import javafx.scene.text.Text;
import javafx.scene.control.Button;
import javafx.scene.control.Label;
import javafx.scene.control.TextField;
import javafx.scene.control.Menu;
import javafx.scene.control.MenuBar;
import javafx.scene.control.MenuItem;
import javafx.scene.input.KeyCode;
import javafx.scene.input.KeyCodeCombination;
import javafx.scene.input.KeyCombination;
import javafx.scene.layout.HBox;
import javafx.scene.layout.VBox;
import javafx.scene.layout.BorderPane;
import javafx.scene.layout.GridPane;
import javafx.stage.Stage;

public class TicTacToe extends Application {
    private static TicTacToeSquare[] board = new TicTacToeSquare[9];
    private static int boardTracker;
    private static StringProperty xPlayer = new SimpleStringProperty("X player");
    private static StringProperty oPlayer = new SimpleStringProperty("O player");
    private static IntegerProperty xScore = new SimpleIntegerProperty(0);
    private static IntegerProperty oScore = new SimpleIntegerProperty(0);
    private static IntegerProperty tieScore = new SimpleIntegerProperty(0);
    private static boolean scoreDisplayed;

    public static void main(String[] args) {
        launch(args);
    }

    @Override
    public void start(Stage stage) {
        BorderPane root = new BorderPane();

        MenuItem newGameItem = new MenuItem("_New Game");
        newGameItem.setAccelerator(
            new KeyCodeCombination(KeyCode.N, KeyCombination.SHORTCUT_DOWN));
        newGameItem.setOnAction( e -> newGame());

        MenuItem exitItem = new MenuItem("E_xit");
        exitItem.setOnAction(e -> Platform.exit());

        Menu gameMenu = new Menu("_Game");
        gameMenu.getItems().addAll(
            newGameItem,
            exitItem
        );

        MenuItem addItem = new MenuItem("_Add player name(s)");
        addItem.setAccelerator(
            new KeyCodeCombination(KeyCode.A, KeyCombination.SHORTCUT_DOWN));
        addItem.setOnAction(e -> addName());

        Text xText = new Text();
        xText.textProperty().bind(
            Bindings.concat(xPlayer).concat(" wins ").concat(xScore.asString()));

        Text oText = new Text();
        oText.textProperty().bind(
            Bindings.concat(oPlayer).concat(" wins ").concat(oScore.asString()));

        Text tieText = new Text();
        tieText.textProperty().bind(
            Bindings.concat("Ties: ").concat(tieScore.asString()));

        VBox scoreLayout = new VBox(5);
        scoreLayout.getChildren().addAll(xText, oText, tieText);
        scoreLayout.setPadding(new Insets(2));
        scoreLayout.setAlignment(Pos.CENTER);

        MenuItem trackItem = new MenuItem("_Toggle score display");
        trackItem.setAccelerator(
            new KeyCodeCombination(KeyCode.T, KeyCombination.SHORTCUT_DOWN));
        trackItem.setOnAction(e -> {
            if (!scoreDisplayed) {
                root.setRight(scoreLayout);
                scoreDisplayed = true;
                stage.sizeToScene();
            } else {
                root.setRight(null);
                scoreDisplayed = false;
                stage.sizeToScene();
            }
        });

        MenuItem resetItem = new MenuItem("_Reset score");
        resetItem.setAccelerator(
            new KeyCodeCombination(KeyCode.R, KeyCombination.SHORTCUT_DOWN));
        resetItem.setOnAction( e -> {
            xScore.set(0);
            oScore.set(0);
            tieScore.set(0);
        });

        Menu scoreMenu = new Menu("_Score");
        scoreMenu.getItems().addAll(
            addItem,
            trackItem,
            resetItem
        );

        activateMnemonics(
            gameMenu,
            newGameItem,
            exitItem,
            scoreMenu,
            addItem,
            trackItem,
            resetItem
        );

        MenuBar menuBar = new MenuBar();
        menuBar.getMenus().addAll(gameMenu, scoreMenu);
        root.setTop(menuBar);

        GridPane layout = new GridPane();
        for (int i = 0; i < board.length; i++) {
            board[i] = new TicTacToeSquare();
            layout.add(board[i].button(), i / 3, i % 3);
        }
        root.setCenter(layout);     

        stage.setScene(new Scene(root));
        stage.setTitle("Tic Tac Toe by Legato");
        stage.show();
    }

    public static void evaluateBoard() {
        for (int i = 0, j = 0; i < 3; i++) {
            // Horizontal
            if(checkSet(j++, j++, j++)) {
                return;
            }
            // Vertical
            if(checkSet(i, i + 3, i + 6)) {
                return;
            }
        }
        // Diagonal
        if(checkSet(0, 4, 8) || checkSet(2, 4, 6)) {
            return;
        }

        if (boardTracker == 8) {
            gameEndPrompt("It's a tie!");
            tieScore.setValue(tieScore.getValue() + 1);
            return;
        }

        boardTracker++;
    }

    private static boolean checkSet(int square1, int square2, int square3) {
        if (boardTracker >= 4) {
            if (board[square1].equals(board[square2]) 
            && board[square2].equals(board[square3])) {
                gameEndPrompt(
                    checkWinner(board[square1].button().getText()) + " wins!");
                return true;
            }
        }
        return false;
    }

    private static void gameEndPrompt(String message) {
        endGame();

        Stage stage = new Stage();
        Label label = new Label(message);
        label.setStyle("-fx-font-weight: bold;");

        Button reset = new Button("New Game");
        reset.setOnAction(e -> {
            stage.close();
            newGame();
        });
        reset.setDefaultButton(true);

        HBox layout = new HBox(5);
        layout.getChildren().addAll(label, reset);
        layout.setAlignment(Pos.CENTER);
        
        stage.setScene(new Scene(layout));
        stage.sizeToScene();
        stage.show();
    }

    private static void reset(TicTacToeSquare[] board) {
        for (int i = 0; i < board.length; i++) {
            board[i].clear();
        }
    }

    private static void endGame() {
        for (int i = 0; i < board.length; i++) {
            board[i].button().setDisable(true);
        }
    }

    private void activateMnemonics(MenuItem... items) {
        for (MenuItem item : items) {
            item.setMnemonicParsing(true);
        }
    }

    private static void newGame() {
        boardTracker = 0;
        reset(board);
    }

    private static void addName() {
        Stage stage = new Stage();
        
        Label xName = new Label("Enter X name");
        GridPane.setConstraints(xName, 0, 0);
        TextField xPlayerField = new TextField();
        GridPane.setConstraints(xPlayerField, 1, 0);

        Label oName = new Label("Enter O name");
        GridPane.setConstraints(oName, 0, 1);
        TextField oPlayerField = new TextField();
        GridPane.setConstraints(oPlayerField, 1, 1);

        Button submit = new Button("Submit");
        submit.setOnAction(e -> {
            String xString = xPlayerField.getText();
            String oString = oPlayerField.getText();
            if (!xString.replaceAll("[^a-zA-Z]", "").isEmpty()) {
                xPlayer.setValue(xString);
            }
            if (!oString.replaceAll("[^a-zA-Z]", "").isEmpty()) {
                oPlayer.setValue(oString);
            }
            stage.close();
        });
        submit.setDefaultButton(true);
        GridPane.setConstraints(submit, 0, 2);

        GridPane layout = new GridPane();
        layout.getChildren().addAll(
            xName,
            xPlayerField,
            oName,
            oPlayerField,
            submit
        );

        stage.setScene(new Scene(layout));
        stage.show();
    }

    private static String checkWinner(String winner) {
        if (winner.equals("X")) {
            xScore.setValue(xScore.getValue() + 1);
            return xPlayer.getValue();
        } else {
            oScore.setValue(oScore.getValue() + 1);
            return oPlayer.getValue();
        }
    }
}

If you have JRE 8, you may download and run the jar.