Is it normal for my baby to breastfeed and not have a bowel movement for days?

Yes. If a baby is eagerly and happily breastfeeding each day, if he has no tummy aches nor bloating, and if his poops are quite soft, then it is ok for him to poop only once every few days. He is digesting all the breastmilk, and using almost all of it to maintain and grow his body (leaving very little solid material to make poop). The water in the milk is absorbed and later urinated out as pee.
Yes. Usually after the first few weeks the pattern of stooling can change from after every feed to every two or three days, sometimes even longer. If the baby is urinating, gaining weight and is comfortable this is not a problem.

Related Questions

My 6wk old baby has not had any bowel movements since yesterday. This is the third day this week but not in a row. Help! I also breastfeed. Help!?

It's okay. As long as your baby is feeding normally and acting normal, this is ok. A rule of thumb for normal bowel movement frequency for a breastfed baby is 7 a day to once every 7 days. The record in my practice was once every 10 days until just last year, the record was broken -- 16 days! Normal baby!
Normal pattern if. Your baby is feeding ok, not vomiting, fussy, or straining. When babies go through growth spurts they absorb all the breast milk so there is no stool. Make sure when he stools that it is not pellets (constipation).
Relax. Breast babies can do a little smear every feed or a onzie filler every 7-10 days. Breast milk is a well designed food source compared to formula, where more debris is left over after processing. Bottle babies usually go at least daily if not more often. If it is soft when they go it is considered okay, even if delayed.