First things first. Depending on where you live, demolition of a 1,500-square-foot house, for example, can range from $5,000 to $20,000 and possibly cost more if there are environmental issues involved such as asbestos abatement. You'd first be required to send a letter to adjoining neighbors informing them of your plan; if there are objections, that could delay or even scuttle the process.
The site must be fenced off and secured for safety and to contain construction dust or sediment. Then there are various city or county permits you'd need to pull and sizable hauling and dumping fees. Utility infrastructure to the house would have to be properly disconnected and terminated at the source. If the house is in a historic district, expect far more red tape.
But this issue is possibly bigger: Most mortgage agreements do not allow you to demolish a mortgaged home because you'd be destroying the only security for that loan. So financing could be a real challenge. With some lenders, you might be able to negotiate a deal using other collateral -- your hopefully equity-laden current house for example -- or a heavy amount of cash, or a combination of equity and cash.
Your strategy is not totally unheard of. In fact, a Marin County couple recently spent $4 million to buy an estate that blocked their view of the San Francisco skyline and Golden Gate Bridge so they could demolish the place.
You should know that zoning regulations could prevent you from eventually constructing, say, only a pool or tennis courts on that separate lot since it's likely zoned for single-family construction only. So to build anything other than a house there, save for a fence, you'd have to get the land rezoned, which could slow the process to a crawl.
Additionally, is there a homeowners association, or HOA, governing your subdivision? If so, HOA bylaws can be even more restrictive than local zoning laws about what gets built and knocked down.
Obviously, you should run your plans by the city or county and any HOA well before you offer to buy the neighbor's house, plus consult with an experienced demolition contractor who has good marks from the Better Business Bureau and such review entities as Angie's List. You might also visit TearDowns.com for more information.