At 4 p.m. in the afternoon on opening night, I got a call from an actress with a medium sized role saying that she was very sick (this was not stage freight either as she was experienced); she was vomiting and couldn't stand up she was so dizzy. We had no understudy so who would know the blocking enough to go on? I did with a book and it was fine. People in the audience said that after a few seconds they forgot I had the book. Of course I kind of knew many of the lines but not in order.  I was the witchey character in A Bad Year for Tomatoes and in one scene had to read the star's hand. It was awkward trying to hold the book and her hand so I just said (out loud) "It is really hard to read your palm with this darn book in my hand and it broke up the audience." Even though I felt bad for the sick actress it was kind of fun to be on stage again. She was back to the show and feeling fine the next night.  

I've done plays with understudies and without. We've never had to use an understudy, but I've been in two plays where we ended up needing one and didn't have one. The first  - one of the leads family members had died, and the funeral was placed the only night we performed. We asked one of our extras to step up, and she learned the lines and blocking, character, etc. in one night. She did an amazing job, but it was rather scary as well, and we could've used an understudy. The second- one of our leads had run into a set piece during one of our matinees. His knee was twice it's size within a few minutes, and the night was very stressful, as we weren't sure he'd be able to go on. Fortunately he was, but having an understudy would've been very reassuring.
 
But like I said, we've done shows with understudies, and never used them. So it's sort of a win/lose, good luck either way.