We did it awhile back. Did the Netflix, Hulu + and HBOGo on an apple tv. Make sure you get a good antenna, if need be an outdoors one (if possible). Paid for 50mbps internet to make sure streaming HD was no issue, while being able to run other devices/comps at the same time on wifi. If you can AppleTV allows an ethernet cord so you connection would be much more reliable (not sure about Roku and Chromecast), if possible go that way! Find someone with BTN, HBO, ESPN...etc that will let you steal their password to use those apps. A lot of ISPs offer ESPN3 now anyway so you would probably be covered at least for a good chunk of sports. We spent:
AppleTV - $75 (sale) 1 time fee
Internet - $19.99 (12 month promo)
Netflix - $7.99
Hulu - $8.99
Antenna - $39.99 1 time fee
So all for under $50, no issues streaming ever and anything we couldn't get we could either find free online (bootleg obviously) and plug into TV.
Or just head to a friends house for a game
or even better your local sports bar. Really was worth it....sadly wife wanted to head back to hear DVR

so we are back up to $120 a month for cable package.
I forgot to mention, which I might try to cut the cord again...they have an OTA Tivo DVR! Technology looks pretty sweet.