The one that tells you the gate is closed when you first want to enter, it gives you the option to intimidate but I don't think there's any way you can actually intimidate him... It must be scripted to not be intimidated but still give you the option for roleplaying reasons or whatever.

Is it possible? And if so, are there any videos of it? I want to know how he'd react.

I believe he can be intimidated, but the check requires a higher speech level than the persuade option. I normally just persuade him because it always works.

Well I used console to give myself the intimidation perk and 100 speech but it didn't work, so...

Some NPC's can't be intimidated, they just dont fear you. Others can't be persuaded because they just dont like you. Its normal.

Intimiadtion chance is also contingent on your overall level. Try leveling yourself up to max, getting max speech, maxed out intimidation perks, then try again.

He has a good argument, like hes going be scared of a lone wanderer when hes got a legion of guards at his back. It must take some high speech to convince him... maybe try wearing daedric?

I'm pretty sure you can't, you can't riften guard for sure, used +50 speech potion, was max level, all speech perks and had an item that improved speech, after it didn't work I did what I told him I do with thieves, shame I couldn't dead thrall him :/

Intimidate success chance is determined by your Speech AND your level as far as I know. Try maxing your level and speech and see if it works.

I've been wondering about this aswell.. I've made some searches and found no reports of successful intimidations to thieves, the whiterun and riften gate guard...

I tried with 100 speech and all speech perks it does not work I tried it on the riften guard and it did not work either. It does work on black briar, logrolf and the bandits/theives that try and rob me but then I just kill them anyway.

There is no response for a successful intimidation with that guard, which means that you cannot intimidate him no matter what. Similarly, that persuade attempt will always work because it's not checking your speech skill at all.

Certain bribery, intimidation, or persuasion attempts are impossible -- the option is merely flavor dialogue, although most checks can either succeed or fail, depending on skill.