Most likely, as others have mentioned, a unbalanced blade, i like to put them on a screwdriver as i sharpen them to balance it out. (hold handle, place blade center hole over driver tip, observe balance)
Also possible that your shaft is bent, but you would remember hitting something with it. You may also have a partially sheared key-way in the flywheel or blade adapter.
Make sure you put the blade on in the correct direction. (happens a lot) Muncher or split blade types placed on backwards can also cause vibrations, as well as sucking big time at mulching and creating vacuum. I don't know why this causes vibes, but it does.
Be safe! Lawnmower accidents are common and typically result in a lost limb or digit. Un plug the spark plug!
As far as operating without a blade goes, it's fine, it just usually has a significant kick-back when pull starting due tot he reduction in rotating mass to absorb the rapid revolution changes.
