S-99: Ninety-Nine Scala Problems - http://aperiodic.net/phil/scala/s-99/

p01.scala

def last(xs: List[Int]): Int = {
  if (xs.tail.isEmpty) xs.head
  else last(xs.tail)
}                                         //> last: (xs: List[Int])Int

p02.scala

def penultimate(xs: List[Int]): Int = {
  if (xs.tail.tail.isEmpty) xs.head
  else penultimate(xs.tail)
}   

p03.scala

def nth(n: Int, xs: List[Int]): Int = {
  def loop(xsA: List[Int]): Int =
    if (xsA.length + n == xs.length) xsA.head
    else loop(xsA.tail)
  loop(xs)
}

p04.scala

def length(xs: List[Int]): Int = {
  def loop(xsA: List[Int], acc: Int): Int =
    if (xsA.isEmpty) acc
    else loop(xsA.tail, acc + 1)
  loop(xs, 0)
}