Should I go by myself to the hospital when my water breaks, or wait for my husband?

If everything has been fine during your pregnancy, none of the complications mentioned below are present and you don't have a history of fast labors, waiting is fine. Remember that the membranes that break are a protective layer for your baby, so it is still better to get to the hospital within a couple of hours of the bag of waters breaking.
Normally OK to wait. If you have had any complications like placenta previa, polyhydramnios, abruption, breech or transverse baby position, you should get to the hospital asap. If you are less than 34 weeks pregnant, the baby hasn't been moving normally or the fluid is any other color than clear like water, you need to go straight to the hospital.