According to the American Cancer Society, yes.
Not having children or having them later in life: Women who have had
not had children, or who had their first child after age 30, have a
slightly higher risk of breast cancer. Being pregnant many times and
at an early age reduces breast cancer risk. Being pregnant lowers a
woman's total number of lifetime menstrual cycles, which may be the
reason for this effect.
In addition, not having breast fed also appears to be a cause:
Not breast-feeding: Some studies have shown that breast-feeding
slightly lowers breast cancer risk, especially if the breast-feeding
lasts 1½ to 2 years. This could be because breast-feeding lowers a
woman's total number of menstrual periods, as does pregnancy. But this
has been a hard area to study. In countries such as the United States,
breast-feeding for this long is uncommon.
They could be linked; I'm not sure if the studies could find women who had never breast fed but also had children.
EDIT According to this study in 1983, the first birth is protective, but later first birth has a potential for higher risk. A further study done in Danes found that if the first childbirth is done between the ages of 20 and 29, then that's the best for risk reduction:
After adjusting for age and stage of disease (tumour size, axillary
nodal status and histological grading), the number of full-term
pregnancies was found without prognostic value. However, women with
primary childbirth between 20 and 29 years experienced a significantly
reduced risk of death compared with women with primary childbirth
below the age of 20 years [20-24 years: relative risk (RR) = 0.88, 95%
confidence interval (CI) 0.78-0.99; 25-29 years: RR = 0.80, 95% CI
0.70-0.91].
Presumably, the study did not contain any statistically significant sample of women older than 29 for their first childbirth to make relevant statistical comparisons.
EDIT 2 In response to @Hendy's comment, here's some further research, done in 1986:
Nulliparous women with a family history of breast cancer had a
relative risk of 2.7 (95% Cl = 1.4–5.2). Women with a family history
who first gave birth by age 20, between ages 21 and 29, and after age
30 years had relative risks of 0.53, 2.1, and 4.0, respectively (95%
Cl = 0.08–3.8, 1.1–3.9, and 1.8–9.6, respectively).
These risks are relative to the 1.0 risk from a study done in Connecticut. Note the direct contradiction with the study Danish study; this later study was performed at Vanderbilt Hospital in Nashville, Tennessee, and found that risk was less in younger women, while the opposite was apparently true in Denmark. The difference in timing (the latter study done in 1986, the former in 2006) may also indicate that changes in breast cancer treatments are affecting population dynamics, but that's pure conjecture.
The causal risks to check for are carcinogens (such as increased estrogen that can be linked to obesity) followed by family history, or, in other words, genetic predisposition to the disease. Mutations in the BRCA1, BRCA2 genes and other genetic markers (TP53, PTEN, STK11/LKB1, CDH1, CHEK2, ATM, MLH1, and MSH2, ibid; BRCA1 and 2 are the most 'famous') are known causal genetic links to having the disease. The effect of childbirth or lactation appears to be difficult to make anything other than a correlative rather than causal link.
Anecdotally, the doctors I worked with all suggested that lactation was the real protection, because without it, the breasts have no real biological function. Lactation made sure they got some use, the thinking went, and so the cells were put to work and weren't sitting idle, making cancer instead of milk. They may have been just yanking my chain, though.
