The question of whether to include the year or not simply comes down to the information you choose to communicate.
If you include years on your resume, you can demonstrate some positive things:
- you've worked professional shows for several years; you're serious about this being a theatre professional.
- you've worked consistently (several shows a year, with little "down time" between shows); you can and do make your living this way.
- you were a resident with a company for several seasons; you are reliable, and people generally don't mind being with you for months at a time.
Dates can share neutral info, and you should be ready to speak to any of these points:
- you have worked musicals (for example) in the past, but not in many years;
- you have taken a bit of a break from the theatre business, either currently or at some point; or
- you don't work often - only a handful of shows every few years.
Or dates can communicate not-so-good information:
- you're either very young or very old (shouldn't be a hiring consideration, I know, but protect yourself if you think this info could make someone think a certain way about you or your ability);
- you're fresh out of school with very little professional/non-academic shows under your belt;
- you only do 1 show or less a year;
- you had to leave a show, or you tend to over-commit yourself (if you show months, or it's clear you have more shows in 1 year than any mortal could handle).
So think about how someone who doesn't know you might look at your resume, and imagine any judgments - positive or negative - they might make about you from what they read on your resume page. You want your resume to be 100% truthful, while presenting your skills and experience in the best possible way. For some individuals, it might be very strong to present dates; For others, it might be very damaging. In some other cases, it simply might just not look well on the page (the aesthetic of a neat, clean page counts for a lot, so cut where you can!). Do what is ultimately best for you.