Rider 1, Rider 2, V3, Skyrider, Kuuga, Agito.
All of these pretty much make it clear that their Rider form is their true self, their human form just being a mask now.
But I found there were many times in which the series implied it was more of an armor. Back in the day, the Double Riders would have an exposed neck, and then there's Hongo's transformation in his bike, seen without a helmet for a moment.
If we are to count SPIRITS I'm not sure what to say anymore.
What THE FIRST and THE NEXT showed us however, is that being a cyborg does not necessarily mean your Rider form can't be an external armor.
I think the same might apply to Kuuga and Agito... well, maybe not Agito.
tl;dr There's no definitive answer for many of the Riders.
My opinions, though:
[HIDE]#1: He has a new body, but his Rider form might not necessarily be the true form of that body.
#2: Ditto.
V3: Ditto.
Riderman: External suit powered by magical science.
X: Maybe a similar case to the first three Riders.
Amazon: New body. Not as biological as other Riders are, though.
Stronger: Same as the first three and X.
Skyrider: Ditto.
Super-1: It seems to be an external armor. But like many other Riders, it's likely the belt is part of his body (that's what generates the suit). Try to take off his helmet, though, and you won't be able to.
ZX: Once again, same as the first three.
BLACK: Unlike the previous examples, his series makes it more obvious his Rider form is his ''true'' form. I think it is a new body in this case. This seems to be the same for Shadow Moon.
BLACK RX: The show might not make it clear, but I think it's the same case.
Shin: New body. I have nothing to say here, really.
ZO: It seems to be a new body. ZO is in many ways a family-friendly version of Shin.
J: Man, I need to rewatch the movie. It might be either.
Kuuga: And yet again, same as the first three.
Agito: I believe it's a new body, same goes for Gills and Another.
G3-X: Armor. I have nothing to say here, really.
Ryuki Riders: Well, when they transform everything appears to be external, from the belt to the suit. I'd say it's armor.
Faiz: I'd say it's an armor. It's what the cyborg Riders might be, which is to say:
-They lost their humanity and gained a new body.
-This body, however, is not their Rider form. The Rider suit is just a way of bringing out their full potential.
Kaixa: Well, it's an armor. I felt like listing it separately because the system works a bit different.
Delta: It works with anybody, I'd say it's an armor too.
BOARD Riders: It's pretty clear they're armors.
Chalice: It's pretty clear it's a new body.
Oni Riders: Another mystery. At first you'd think they are new bodies, but then there's all that technology and how that's the only way they can reach their forms. I'm really not sure here, it can be either one. That oni armor that appeared in the Shuki episodes seems to imply their oni forms are another body (why would they need an armor like this?).
Kabuto Riders: Armor, it seems. Just like I said with Ryuki & co.
Den-O: It has to be an armor, the imagin can access it too.
Zeronos: Even with what happened with Zero form, this might be an armor too.
Kiva/Dark Kiva: I daresay, this is a new body. Although the way the Fangire King uses it even though he already has a Fangire form, it might be the same case as with Faiz. Could be either, though.
IXA: Pretty clear it's an armor.
Saga: Same as Kiva? Not reallly sure here.
Decade: Back in some old thread, I think NeonZ posted some fun facts about how Decade seemed to be intended to be a cyborg and in Ganbaride he says: ''This is my true form.'' There's that weird transformation at Movie War 2010 too. For now, I'll play it safe and say it's an armor.
If he is a cyborg however, well... see the first three and Faiz again.
Diend: Armor. I don't think Kaito is a kaizo-ningen, though he might as well be with how high he jumps.
W: Excluding Xtreme, I think it's an armor, even with what Philip is (see the first three Riders and Faiz). Now as for Xtreme, that one form might be a new body, which is the fusion of their two consciences; either that or it's an armor contaning both bodies.
Rest of W Riders: Pretty sure it's armor for all of them. I will go ahead and say the Dopants might be a new body, even when using belts.
OOO: Could be either, really. It depends a lot on the user.
Births: Armor. They make it clear with some nice shots.
Poseidon: He's worth a mention. Basically it's a lesser Greeed that at first depends on a user and so puts on the armor intended for Miharu. But later becomes it's own body, based on that armor... well, if it was an armor.
Aqua: Worth a mention too. You'd think he has a new body, but the belt is external. It's highly likely this is what I theorized with Faiz.
Fourze: Armor.
Meteor: Ditto.
Wizard: Could be either, really.[/HIDE]