Rather than answering this question myself, I’m going to refer you to this great answer by Dr. William Berkson, director of the Jewish Institute for Youth and Family, which originally appeared in Reform Judaism magazine. Though Dr. Berkson is not a rabbi, his answer is spot-on.
The Bible says yes. The "rebellious son" is to be put to death by stoning (Deut. 21:18-21), and Proverbs (13:24) teaches: "He who spares the rod hates his son."
But by the talmudic period, these harsh doctrines of parental discipline were replaced with an emphasis on kindness and compassion. The Talmud defines the "rebellious son" out of existence (San. 71a), rules that a teacher could punish a student at most with a leather shoelace (Bava Batra 21a), outlaws hitting grown children (Mo'ed Katan 17a), and declares: "With a child, push away with the left hand, and draw near with the right" ( Sotah 47a)--the right hand normally being the stronger. As a result of these rabbinic teachings, traditional Jewish homes were noted for treating their children with love and warmth. Still, corporal punishment was not eliminated in the traditional religious school for boys--the cheder--in Eastern Europe, where teachers often hit their students for even minor infractions.
Modern social science is still divided on the question "to spank or not to spank." In 1996, Dr. Murray A. Straus, a professor at the University of New Hampshire, and Dr. Robert Larzelere of Boys Town began a continuing debate in the journal Pediatrics on the effectiveness of spanking. Dr. Straus argued that many studies, including his own, show that spanked children become more antisocial and do worse in school. Dr. Larzelere challenged Straus's conclusion, claiming that the damaging effects of spanking are true only in cases of frequent spanking and of corporal punishment of older children. For two- to six-year-olds, he wrote, occasional non-abusive spanking ("two open-handed swats to the buttocks leaving no bruise") is beneficial as a back-up to time-outs and reasoning; when the children turn seven, time-outs and reasoning alone--with spanking in reserve--have become so effective that spanking is no longer necessary.
Both sides of the debate agree that spanking school-age children is undesirable. As for toddlers, nearly half of American parents oppose spanking, but, according to Straus, nearly all resort to corporal punishment on occasion. With the debate on disciplining toddlers still unsettled, a good Reform Jewish approach would be to err on the side of compassion and follow Straus's advice never to spank.