What about a cell phone or cable bill?
Okay, you really need to get a copy of your credit report! It is sooo empowering to see a record of your business history (and even more so to see it improve over the years).
No, cell phone and cable records do not appear. But neither do lease agreements! All of your past addresses, or at least some of them, will--any address you had at the time you had an account. But it is just the mailing address, nothing about whose name was on the lease or whether you owned or rented. If you were evicted, that court action will appear. If you were late enough that the rent was sent to collections, that will show, but as a debt to the collection agency, not as a landlord. When you apply for an apartment, the landlord will ask for your previous addresses, and you can provide them, even if your name wasn't on the
lease. When they check your credit they are usually looking for evidence of evictions and a match to the addresses you provided on the application.
Where did you live when you were collecting student loans? Did you live on campus by any chance? Because if so, you had a rental agreement with the Housing Department of the school, and that is rental history.
I think you may be presuming that your credit is worse than it is, just because you haven't seen your own credit report. You can get a free credit report every year from each of the three agencies at www.annualcreditreport.com (say 'no thanks' to their offers to sell you additional products, just get the free ones).
As far as housing goes, the wait lists are extremely long, at least 7 years. I am not making this up, in fact there was a news story done here on this recently.