We don't own a TV, and don't have cable. We do, however, have the Intertubes! As a result we get to be selective about what we watch. There's some damn good TV available and we've been able to catch up with some of it by Netflix or DVD.
Shows we're keeping up with now or have recently watched are:
Downton Abbey (although it's getting more difficult to care about anyone other than the Dowager Countess)
Game of Thrones
Gracepoint (we're mostly watching this one so we can try to identify where each scene was shot!)
Breaking Bad (pretty much watched this late at night while bottle-feeding Erik. Hope it doesn't affect him)
Call the Midwife (this one may also be nearing its best-before date)
Doctor Who (started with the Christopher Ecclestone series, and am now halfway through the Matt Smith years)
Watched the first season of Walking Dead, decided I didn't want to continue.
Further suggestions welcome, but bear in mind that I can only fit in one or two hours per week and I've still got a bit of Doctor Who to get caught up on!