Bill Cork has an excellent discussion of Eucharistic ministers and the nature of the Eucharist.
I served as an extraordinary Eucharistic minister for 6 years. Too long, in my opinion. I decided to resign last year because I could detect a sense of habit and routine setting in. This duty cannot be performed by habit or routine. I cannot take it for granted, so I needed to step back, even though there is a shortage of people to serve as EEM's. It's better not to do this duty than to do it poorly.
I look upon this duty as me simply serving as the extensions of the hands of the priest. He just didn't have enough hands to go around, and I am contributing my hands during a time of priestly shortage. Someday, the EEM will no longer be needed.
Even so, I was often overwhelmed by emotion after serving as an EEM. The faith of those who receive is radiant on their faces and my own poor faith is put to shame. Oh yes, there is the many casual recipients and many who I suspect do not have a clue or care about what they are doing. That is mostly not my call, but I do report any abuses, general lack of reverence or other problems to the priest.
I attempt to be "invisible" to the recipient. This is a meeting between the person and God. I just happen to be nearby. I try to be both reverent and unnoticed but will not hesitate to climb over pews to deliver the Body of Our Lord to an elderly or handicapped person who cannot go up to the altar.