jessamy80,
By definition, general endotrachial anesthesia is an anesthestic that puts the patient so deep into sedation that the respiratory centers do not function, and as such, the patient has to be intubated (breathing tube down throat, with machine breathing for you).
The biggest risks associated with GEA is during the induction phase, or when the patient is "put under". If the patient develops a bronchospasm, the tube may not be able to be placed. This, of course, would affect oxygenation of the tissues. If an airway is not established somehow quickly, brain injury due to anoxia can occur. How often does this happen? Very, very rarely.
The other risk is the manifestation of a previously undiagnosised medical problem. On occasion, the patient may have, for example, a cardiomyopathy, which has not really been a problem. But, when he/she is put under the stresses of anesthesia, the disorder shows itself. If the condition is serious enough, it can cause problems (death). This is much more common in children, then in adults. And, again, it is very rare.
Another is reaction to medications. But, this can occur with any anesthetic.
You can have regional anesthesia with sedation. Where a block is given for pain control, but the patient is sedated, so that he/she sleeps. But, it is not so deep of a sleep that he/she cannot control his/her own airway. The patient breaths on his/her own.
Conscious sedation is just enough sedation so that the patient doesn't really care what is going on. Problem here, the patient may move around. Pain control is not quite as good, but the patient is usually amnestic to the events. Though he/she may speak to the personel in the OR, he/she will not remember anything.
All anesthesia carries risks and benefits.
Like brittntc stated, these are questions you should ask of your surgeon and anesthesiologist. Before any procedure there has to be an anesthestic evaluation. This may be done by an anesthetist (nurse or PA), it is done under the supervision of an 'ologist (anesthesiologist). This is the time to ask any and all questions.
Most of the time, unless the surgery calls for a specific type of anesthesia, the surgeon will allow "patient's choice". Again, some cases have to be done under general, because relaxation of the muscles is required, so a paralytic agent has to be given. Thus the patient could not breath on his/her own. Other procedures have to be done under local with sedation, because the patient has to be aware during the procedure (many brain surgeries are done this way).
Again, it depends upon the procedure, surgeon's choice, patient's overall health, and the patient's choice.
So, discuss all of your questions and concerns with the anesthesia staff prior to the procedure.
Good luck.