Here are my expected turn around times during regular business hours and excluding weekends holidays, and out of office replies. This is also the order in which I escalate communications...
* Email: Within 24 hours
* Instant Message/Chat: Immediately, Within 2 hours.
* Phone: Immediately, return a voice mail within 4 hours.
* Scheduled meeting: Give at least 24 hour notice.
If you really need a response, pick up the phone, multiple times if necessary. You could also schedule a meeting with the person. For some people/situations I know I will need to include someone else on their team, sometimes a supervisor, to get any traction.
You should escalate on the third non-response by including their supervisor on an email, group chat, or meeting. Include previous communications with dates. Take this advice with a grain of salt and take into account previous interactions with the person of course.
If you have a ticketing system, copy and document each communication into the system. In some situations you may want to start with the ticketing system even if you could send the request directly to the person to begin with.