This is going to be one of the most common situations, statistically speaking. The tough problem is...your neighbors might not tell you! Moral of the story - make friends with your neighbors!
Scientists have studied the density of termite colonies and have found, on average, 2-4 colonies per acre. This study was performed in North Carolina, which is a similar termite environment to DFW.
So, it's highly likely that we're dealing with termites on or near your property.
If your neighbors have termites, that means the colony may extend physically to your property and become an issue. Good news is that once termites find a food source, they may just be satisfied with exhausting that food source. However, studies have shown that termites from one colony will travel more than 1 whole acre to find a food source…So, chances are, you’re within 1 acre of your neighbor and should be on alert.
In this situation, I'd highly recommend a treatment or, at the very least, a thorough inspection on a regular basis to try to catch an issue early on.
But, you may have termites and don't know it as they can be silent killers (i.e., they’re behind the walls and you don’t see them). Inspections, even thorough ones performed by professionals, aren't guaranteed to find termites since (as I’m sure you’d agree) you don’t want us tearing out walls and ripping up floors looking for them. Because of that, there's no guarantee that an inspection will unearth termites even if they are there.
Best Types Of Termite Treatments For Homes
Given the risk, I'd recommend that you do a treatment if your budget allows. The best type of treatment for preventative / suspected situations is a bait station treatment such as Sentricon given the balance of cost and effectiveness at colony elimination (read more on these types of treatments here).
If your neighbors are doing a traditional liquid treatment - I'd be more likely to recommend that you treat because liquid treatments typically do not eliminate the colony, just put up a barrier (like a moat) around their house, which is more likely to drive them away.
If your neighbors are doing a bait station treatment - you might be able to get away with not doing one as baiting stations are designed to eliminate the colony, rather than just push them away.
But either way, it's going to be risky to not treat. So you have to ask yourself, "Do I feel lucky?" Well, do ya?