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Group.cs

using UnityEngine;
using System.Collections;

public class Group : MonoBehaviour {
    // Time since last gravity tick
    float lastFall = 0;

    void Start() {
        // Default position not valid? Then it's game over
        if (!isValidGridPos()) {
            Debug.Log("GAME OVER");
            Destroy(gameObject);
        }
    }

    void Update() {
        // Move Left
        if (Input.GetKeyDown(KeyCode.LeftArrow)) {
            // Modify position
            transform.position += new Vector3(-1, 0, 0);

            // See if valid
            if (isValidGridPos())
                // It's valid. Update grid.
                updateGrid();
            else
                // It's not valid. revert.
                transform.position += new Vector3(1, 0, 0);
        }

        // Move Right
        else if (Input.GetKeyDown(KeyCode.RightArrow)) {
            // Modify position
            transform.position += new Vector3(1, 0, 0);

            // See if valid
            if (isValidGridPos())
                // It's valid. Update grid.
                updateGrid();
            else
                // It's not valid. revert.
                transform.position += new Vector3(-1, 0, 0);
        }

        // Rotate
        else if (Input.GetKeyDown(KeyCode.UpArrow)) {
            transform.Rotate(0, 0, -90);

            // See if valid
            if (isValidGridPos())
                // It's valid. Update grid.
                updateGrid();
            else
                // It's not valid. revert.
                transform.Rotate(0, 0, 90);
        }

        // Move Downwards and Fall
        else if (Input.GetKeyDown(KeyCode.DownArrow) ||
                 Time.time - lastFall >= 1) {
            // Modify position
            transform.position += new Vector3(0, -1, 0);

            // See if valid
            if (isValidGridPos()) {
                // It's valid. Update grid.
                updateGrid();
            } else {
                // It's not valid. revert.
                transform.position += new Vector3(0, 1, 0);

                // Clear filled horizontal lines
                Grid.deleteFullRows();

                // Spawn next Group
                FindObjectOfType<Spawner>().spawnNext();

                // Disable script
                enabled = false;
            }

            lastFall = Time.time;
        }
    }

    bool isValidGridPos() {
        foreach (Transform child in transform) {
            Vector2 v = Grid.roundVec2(child.position);

            // Not inside Border?
            if (!Grid.insideBorder(v))
                return false;

            // Block in grid cell (and not part of same group)?
            if (Grid.grid[(int)v.x, (int)v.y] != null &&
                Grid.grid[(int)v.x, (int)v.y].parent != transform)
                return false;
        }
        return true;
    }

    void updateGrid() {
        // Remove old children from grid
        for (int y = 0; y < Grid.h; ++y)
            for (int x = 0; x < Grid.w; ++x)
                if (Grid.grid[x, y] != null)
                    if (Grid.grid[x, y].parent == transform)
                        Grid.grid[x, y] = null;

        // Add new children to grid
        foreach (Transform child in transform) {
            Vector2 v = Grid.roundVec2(child.position);
            Grid.grid[(int)v.x, (int)v.y] = child;
        }
    }
}

grid.cs
using UnityEngine;
using System.Collections;

public class Grid : MonoBehaviour {
    // The Grid itself
    public static int w = 10;
    public static int h = 20;
    public static Transform[,] grid = new Transform[w, h];

    public static Vector2 roundVec2(Vector2 v) {
        return new Vector2(Mathf.Round(v.x),
                           Mathf.Round(v.y));
    }

    public static bool insideBorder(Vector2 pos) {
        return ((int)pos.x >= 0 &&
                (int)pos.x < w &&
                (int)pos.y >= 0);
    }

    public static void deleteRow(int y) {
        for (int x = 0; x < w; ++x) {
            Destroy(grid[x, y].gameObject);
            grid[x, y] = null;
        }
    }

    public static void decreaseRow(int y) {
        for (int x = 0; x < w; ++x) {
            if (grid[x, y] != null) {
                // Move one towards bottom
                grid[x, y - 1] = grid[x, y];
                grid[x, y] = null;

                // Update Block position
                grid[x, y - 1].position += new Vector3(0, -1, 0);
            }
        }
    }

    public static void decreaseRowsAbove(int y) {
        for (int i = y; i < h; ++i)
            decreaseRow(i);
    }

    public static bool isRowFull(int y) {
        for (int x = 0; x < w; ++x)
            if (grid[x, y] == null)
                return false;
        return true;
    }

    public static void deleteFullRows() {
        for (int y = 0; y < h; ++y) {
            if (isRowFull(y)) {
                deleteRow(y);
                decreaseRowsAbove(y + 1);
                --y;
            }
        }
    }
}

spawner.cs
using UnityEngine;
using System.Collections;

public class Spawner : MonoBehaviour {

    // Groups
    public GameObject[] groups;

    public void spawnNext() {
        // Random Index
        int i = Random.Range(0, groups.Length);

        // Spawn Group at current Position
        Instantiate(groups[i],
                    transform.position,
                    Quaternion.identity);
    }

    void Start() {
        // Spawn initial Group
        spawnNext();
    }

    // Update is called once per frame
    void Update () {

    }
}