Do you "prevent somebody doing something", or "prevent somebody [from] doing something?

I think unnecessary and redundant are somewhat "loaded" terms in this context. In fact, we usually do include the preposition "from"...

...and I think only a pedant would argue for or against any of those three, in almost all contexts.

Comparing UK/US-only usage on that NGram suggests Brits may be slightly more likely to omit "from", but that hardly seems significant. The main factor affecting usage for all native speakers is that we're more likely to drop the preposition in simple constructions. Thus...

"You can't prevent me going!"

...is immediate and unambiguous (though many of us might prefer "stop"). On the other hand...

"You can't prevent an unemployed person watching daytime TV from drinking too much"

...is something of a garden path sentence. I highlighted the word "from" so you'd see it coming.

If I hadn't highlighted the word, you might well have assumed it before "watching". And then been forced to re-analyse later, when you finally came to the actual word explicitly stated. Which could have been even later - I could have written "You can't prevent an unemployed person watching daytime TV drinking too much from dying young" (forget the missing "and's" and commas).

Answer is yes as well as no . If you omit "from", on some occasions, the sentence would still mean the same thing but mostly, it will not be sufficient without "from" to express the meaning. Without "from", the sentence mostly takes a different construction (I'll give examples at the bottom).

It is safe to use "from" to modify the object where required. Without "from" in the sentence construction, an english speaker might need an extra moment to grasp the intent of the phrase. However, I searched on The British National Corpus (BNC) and found that "from" was omitted on many occasions.

Consider in these examples from BNC: "Instinctively, to prevent her falling, I grabbed her hand (it was buttocks on BNC)" and "That did not prevent her from being thrown down a mineshaft to her death in 1918." In second sentence, if you omit "from" the meaning changes completely.

Ref: bnc.bl.uk/saraWeb.php?qy=prevent+her&mysubmit=Go. (You will find hundreds of examples here) though I think its is a recommended to use "from" for a North American.

OOD offers this meaning:

8 Indicating prevention.
'the story of how he was saved from death'

In "prevent somebody from doing something" prevent and from are redundant but not wrong. "Prevent somebody doing something." is less redundant so I would go with that. My rule is don't use two words when one will do.