I have something in my history that might make me inadmissible. Is a waiver possible?

Waivers exist for many grounds of inadmissibility and are commonly filed during consular processing or alongside an adjustment of status application. Which waiver applies, and what it requires you to prove, depends entirely on the ground itself — some turn on hardship to a qualifying relative, others on time elapsed or the nature of the conduct. This is one of the areas where a general answer is genuinely useless: the ground has to be identified first.