Personally, I'm opposed to the idea of eliminating the position. I believe it provides a good constitutional check to the governor. I also like the idea that it is an independent office, and that the Lt. Governor is not just a 'yes man' on the Governor's ticket.
In the early days of the Republic, the vice-president was the person who received the second largest number of delegates in the electoral college. I think we would be very well served to go back to that system on the national level.