How long can you go without getting a crown for a tooth?

Getting a crown. Impossible to say without more information. How long you can wait depends on why the tooth needs a crown, and how much natural tooth structure remains, These are questions you need to ask the dentist who is restoring the tooth.
Waiting to crown. My best answer when asked this question is this.......You crown the tooth the day before it breaks! In other words, no dentist has a crystal ball to adequately answer the question since so much depends on the quality of the restoration already present, the compressive/shear forces placed on the tooth, your current dental hygiene protocol and so on.
Not good to delay... The consequences of delay in implementing needed crown service depends on the circumstances. Failure to repair a broken or decayed tooth can lead to decay progression, pulp exposure and infection, progressive structural loss, drifting of teeth, and ultimately, tooth loss. These issues progress at varying rates, from differing initial tooth conditions. Therefore, any delay should be minimized.
Depends. Did you have endodontic treatment? Is there decay? Does it have an existing crown? There are many treatment protocols, it's best to speak with your dentist. Generally, it isn't a good idea to wait for treatment...Depending on the reason for the crown, you may be able to wait a short period of time (week(s))...But the delay may result in a larger issue than you started with.
Crown. Get the crown ASAP. The longer you wait the more chance that the tooth will break or other problems will get worse. It is impossible to give you a specific length of time.
If. If you wait, and adjacent and opposite teeth collapse into any extant space, you will have to undergo tooth realignment before a crown can be fabricated. In other words, Dentistry isn't expensive, neglect is.
Depends. If your tooth had a root canal, it'll need a crown asap if: it is a back tooth (molar or pre-molar), or if it is a front tooth that has lost a lot of enamel due to fracture or decay. There are many other reasons teeth need crowns that i cannot get into here due to lack of space...