As of the last Legislative session, for the most part, Cities can no longer just annex properties without the owners consent. It was basically a big "Fuck You" to Austin due to the River Place fiasco.
I suspect that Counties will eventually push back on the the lege when they get tired of paying for road maintenance everywhere, but for now, if a City wants to annex a subdivision, they have to get approval from the property owners.
On the issue of annexation/providing service, the City is required to provide water and sewer within a prescribed time frame. I think it is like three years. However, that does not mean they have to connect your house to the system. They just have to make the pipes accessible to your property and then the property owner has to foot the bill for the connections and the system on their property.
It is generally a very slow process, but over time, once the infrastructure is provided, owners/developers that have large lots that had been required to be 1 acre or larger for septic systems, will eventually see the benefit of bulldozing their house, subdividing the lot and attaching to city services.