Position rack in center of oven and preheat to 350°F Spread bread cubes in single layer on large rimmed baking sheet. Bake until pale golden, stirring occasionally, 15 to 20 minutes. Transfer bread to very large bowl.
Sautésausage in heavy large skillet over medium-high heat until cooked through, breaking up into small pieces with back of fork, 8 to 10 minutes. Using slotted spoon, transfer sausage to bowl with bread cubes. Add onions and celery to drippings in skillet; sautéuntil golden brown, about 12 minutes. Transfer to bowl with bread-sausage mixture (do not clean skillet).
Melt 2 tablespoons butter in same skillet over medium-high heat. Add apples; sauté until tender, about 10 minutes. Add to bowl with bread mixture; mix in raisins.
Melt remaining 2 tablespoons butter in same skillet over low heat. Add 2 tablespoons sage; stir 30 seconds. Add sage butter to bowl with bread-sausage mixture; toss to blend. Season stuffing with salt and freshly ground black pepper. DO AHEAD: Can be made 1 day ahead. Cover and chill.
Position rack in center of oven and preheat to 350°F Generously butter 15 x 10 x 2-inch glass baking dish. Whisk broth and eggs in medium bowl; add to stuffing and toss to mix. Transfer to prepared baking dish. Bake stuffing uncovered until top is golden and crisp in spots, 45 minutes to 1 hour. Let stand 10 to 15 minutes and serve.