Typically, what are some factors to consider when applying to away rotations (are they difficult to get into, depending on the hospital)?
Could be difficult, like some have step cutoffs. You'll want to consider proximity and relative cost. You'll also want to consider whether it's even worth doing a rotation there, like if they even interview their rotators. But you just might want a great letter, which is great too. You'll also want to consider how much of each resident class is filled with rotators. That will give you a good idea about how much they weigh aways at their specific institution. You'll also want to consider how easy it is to get a letter from the chair/PD (can you get enough face time?) What's the structure of the away? Four weeks on one service? Two weeks on two? One week on four different services? The longer you work with an attending the better your letter will potentially be.
You'll have to talk to other applicants to your respective specialty, residents at your home institution that just went through the match, and read the specialty specific spreadsheets.
How many do students usually do over the course of their MD education?
I think it's relatively low. Usually the most competitive specialties require them.
Edit: I thought you were asking how many students do them. For how many are necessary, it depends on the field. I know in ortho it's getting out of control. Nowadays people doing a sub-i + 3 aways isn't unheard of.
and what are some specialties for which doing aways is strongly suggested (or also, not especially needed)?
Necessary: ortho, neurosurg, plastics, vascular, CT, +/- IR, uro(?), EM
Not necessary, but can help: ENT, GS, OB/GYN
On top of this, there are people applying for mid tier specialties or noncompetitive specialties that want to match at a top tier institution or in a specific, competitive location. Some want to couples match. Those are other factors to consider.