Obviously, everything we see, read or otherwise experience will influence us at some level.
But I think you mean influencing to a level where elements of TV series are brought to the tabletop.
I'm sure I won't have to mention Crooked Dice's 7TV; it's completely built up out of TV (and film) tropes. So that one system alone will scratch any TV itch.
But on a personal level, there is a very specific example I can mention: Gerry Anderson's UFO.
I'm absolutely in love with that series, and am in the process of converting and building both miniatures and vehicles in 28mm to play in that setting.
That is the only TV series that I'm translating to the tabletop directly though, although there have been some smaller influences like Dr Who, Sharpe, Transformers (G1) and Space:Above and Beyond.
But there have been many other sources that have had a small or larger influence on my miniature collection and games. Interestingly enough though, most of those have been either books or films, and not TV series. In that category, there are Star Wars (of course
), Battletech, Lord of the Rings, the Alien franchise, Mad Max and many more.
I think that's because it's not that easy (or affordable) for TV series to depict large skirmishes or battles, which obviously form the bread and butter of miniature wargames. Instead, TV series, due to the limited format, are much more suited for translation to RPG or small skirmish games.
My UFO game will also fall into the small skirmish category, probably with a limited RPG element. The series simply never depicted actual pitched battles, and the largest force seen on screen must have existed out of a maximum of 10 men. And I think that goes for most TV series, the exceptions I can think of, being Game of Thrones and Rome (obviously due to their huge budgets)...