The Mishna in Moed katan says that a person is not allowed to take a haircut/shave on Chol hamoed. The reason given is so that a person should not come into Yom Tov looking bad. R' Tam holds that of you took a haircut on Erev Yom Tov you can take one on Chol Hamoed, this opinion is not accepted.
II. Nowadays, can someone who shaves everyday shave on חול המועד
There are 3 opinions:
1. It is permitted if needed
2. You are חייב to shave
3. It is prohibited to shave
R' Moshe (אגרות משה או"ח חלק א סימן קס"ג) holds that it is permitted if needed. He says that times have changed, many/most people shave everyday and therefore it is permitted to shave on חול המועד. Even if a person shaved on ערב יום טוב he needs to shave again on חול המועד and everyone knows this. Because there is no way out it is permitted (see the teshuva for all his reasoning).
RYBS takes R' Moshe's position to it's logical conclusion, since you are allowed to shave you are חייב to shave because of כבוד יום טוב of the last day.
Others (see for example shmiras shabbos k'hilchasa volume 2 chapter 53) hold that chazal made a gezera not to cut hair on חול המועד and therefore it applies in any and all cases and the fact that now people shave everyday is irrelevant, just like the prohibition of taking medicine applies on shabbos nowadays even though no one grinds their own medicine.
When I was in R' Willig's shiur as a freshman in YU, this question came up and he answered as follows. he said that the minhag is for yeshiva boys not to shave and he sees no reason to change that. What about כבוד יום טוב? He quoted a line from the Chasam Sofer "ניוולו זהו כבודו" meaning that coming into the last day of יום טוב unshaven is considered כבוד יום טוב because that is the practice. כבוד is a very subjective thing and depends on the time and place. If the minhag is not to shave then that is כבוד.
It comes out that if you hold like the Rav it really depends on where you live. If you live in a place where almost no one shaves (like I do in Israel), then even according to the Rav you could say that you shouldn't shave, it is not כבוד to stand out and be different then everyone else. If you live in a place where everyone shaves then the reverse applies, you wouldn't say ניוולו זהו כבודו and therefore you would be חייב to shave. If you live in a mixed community it would seem that both sevaras apply.
As always ask your Rav what to do.