If you check emails, respond to emails or work while you are on vacation - STOP.
You are literally giving money away to your company. Your company is paying you to not work, so if you work, you are effectively working for free.
Now in some cases people claim they must work but can hedge against that time by representing that on a time sheet, reducing the amount of PTO actually take.
This is slightly better but not OK as you are setting the expectation that you are available during vacation.
Companies and co-workers will abuse this, (John works on vacation so just email or call him). Also, expectations need to be set with employers that you will not be available at all during your PTO.
For example, I tell the client I will not check my email, nor answer my phone and make that clear in my out of office message, proving other contact(s) to reach out to in case of emergency.
Vacation/PTO is extremely important. Companies already get (at least) 40 hours/week from most of us so why give a second more than that?