There are three different types of invisibility discussed in a Dragon Magazine article called Seeing is Believing contained in issue #105, which are physical, psionic and illusion. As psionic is a mind effect for other people, yes, the practitioner would be able to see themselves.
For physical, the only item they state that produces this effect is Dust of Disappearance. The description and interpretation given is:
This magic dust has the power to bend the rays of light as they pass near it. This causes light not to strike the object the dust is sprinkled over,
rendering it invisible because no light reflected from it reaches the eyes of the viewers. This is the only real invisibility in the game, and is also the only power that can turn something non-living invisible. The other spells only affect a single living thing and any possessions being carried.
My interpretation on that is that since it states no light from what is covered in the dust (i.e. the player and their possessions) reaches the viewers eyes, that they would be invisible to themselves. It does state, however, that sound, smell, etc are not affected, so those may indicate the presence of the person/animal using the dust. However, reflected light from other objects will still be available to enable vision.
For illusion, it specifically addresses the viewability:
If my character is invisible, can he see
Yes. The spell is an illusion which the recipient automatically disbelieves and
so, for that matter, does the caster of the spell when the recipient is some other creature. By the same token, neither the recipient nor the caster will be immediately aware of the fact when the recipient becomes visible to others. If some viewers have disbelieved and others havent, the recipient might forget who can see him and who cant, which could cause problems.
It is a fairly detailed review, and goes into comparisons of physical vs mind effects, with DMG references and other supporting information.