I play vanilla...
Let me know how you use the spy.
In Vanilla, they can't die if you don't execute any Missions. This behaviour changed in BtS, where Spies have a chance of dying when they are in enemy territory, but in Vanilla, you can essentially camp Spies in enemy lands for as long as you want and they won't magically disappear.
Of course, if your Spy fails at a mission, it will die, but my favourite use for them is to simply travel from AI City to AI City to see what build items the AIs are making.
It can get very expensive to sabotage production, particularly Space Ship parts that get a lot of production bonuses, so I often first aim to pillage production-based Resource squares and Mines with the Spies, if the build item won't complete in a turn or two, and then will try and sabotage the production.
If you are going to Steal Plans, you'd probably best have a use for them, such as declaring war on the next turn and wanting to know where the AI has its forces stationed. The other main use would be to see what kinds of defenses the AI has, in order to see if your current army will be more than a match for what the AI has. Finding a capital or a City that has Versailles or the Forbidden Palace in it will make this mission cheaper (look for a small star icon next to the City's name on the main game screen for the latter two types of Cities--or better yet, use the F9 -> Wonders screen to figure out where Versailles is located).
I've also noticed sometimes that the cost of City-based misisons seems to go up over time. I haven't looked too deeply into this concept, but I imagine that a value that often increases, such as the City's Culture level or the City's population is factored into the cost... meaning that you might be better off Stealing Plans out of the AI's Forbidden Palace City (if it has one) than out of the AI's capital itself.
If your plan is to disconnect Strategic Resources, I wouldn't bother most of the time, unless you plan to declare war within a couple of turns. Usually by the time that you can build Spies, the AIs have so many taskless Workers sitting around that they can quickly rebuild the improvements at no additional cost. At least if you go into war shortly thereafter, particularly if you station some units near the relevant City that controls the Resource, the AIs may run their Workers away and thus might not rebuild the crucial improvements, leaving them without Oil or Uranium or whatever. However, disconnecting such Resources in peacetime with the hopes of preventing the AIs from building the relevant units doesn't tend to be a viable strategy, since their Workers can get in there so quickly and rebuild the relevant improvement... to the point that after the first rebuilding effort, there will be so many idle Workers "standing by" the area that the second and subsequent rebuilding efforts will occur far more quickly than the first one.