By the time your child is a toddler, he will have chosen some favorites from the ones you sang or shared with him as a baby.  Continue to sing and share these favorites.  My toddler loves Somewhere Over the Rainbow.  I sing this to her every day at her nap time and she now (20mths old) can sing along with me, getting many of the words correct.

I would also recommend beginning to sing the ABC song as a lullaby to your toddler daily.  Sing softly and with a lilt.  By the time your child is 2 she will be familiar with the names of the letters, and ready to be taught to recognize them.  

For the second year of a child's life I have chosen to focus on sharing lullabies from around the world.  There are a number of CDs available with lullabies in foreign languages.  I have listed these resources below.

For each of the 24 lessons I have suggested a lullaby to share that I have found on CDs available at my library.  You can choose different selections from mine.  There are many beautiful lullabies and I find toddlers greatly appreciate hearing them before a nap and/or bedtime.