No, most of them won't bother you ! It will eventually wear off as the skin grows and you can pick it off. Super-Glue is a little harder to get off but it will do the same thing once it hardens. It will start to come away from the skin in a couple of days and as it gets wet. Then just pick it off ! No long term effects unless you have it all over you and then you better go to the Hospital and see what they can do !
When the skin wears off, the glue wears off. If the glue/adhesive is not something like super glue (an Acrylic/Cynide compound) you can usually get it off with one of the following.. Acetone, Olive Oil, Lacquer Thinner, or an equiv. Typically the glue doesn't "hurt" but it can be a pain if you glue a few fingers together.
The adhesive might cause rashes on some peoples' skin, while on others it won't. However, adhesive will always cause an irritation to the skin and thus make one uncomfortable. This can be removed from the skin by a nail polish remover or by cleaning alcohol.