You need Internet that is at least 1Mbps, preferably 10Mbps (10Mbps is enough to stream 2 sources close to HD, or 1 and browsing the web otherwise, 1Mbps provides enough to stream at SD probably).
I have a HTPC (Home Theater PC), which is superior to most other devices because I can browse the web too along with streaming all kinds of content and playing DVD/Blu-ray movies. Some shows are only available on the networks website and not on other streaming services. If you don't feel like messing with that (buying one, setting it up, installing lots of programs to make it easy to use), a Roku is a very good alternative, but you could also use a "Smart" Blu-ray player. A PS3, XBox, or Wii also works for streaming Netflix if you have them.
I also suggest getting an antenna (rabbit ears may work depending on your location, or you may need to upgrade to something bigger). Then you'll get all the major broadcast networks (ABC, NBC, CBS, Fox, PBS, etc...). If DVR of the major broadcast networks is a necessity, there are options. Aereo is a pay service that provides such capabilities (and you wouldn't need rabbit ears). Another option is HDHomeRun to record what you receive over the air. However, if you can get to the broadcast stations website or Hulu (or pay for Hulu Plus), then you can typically stream the broadcast shows 24hrs after the original airing (the other typical time frame is 1 week + 1 day).
I would suggest saying you try it as an experiment for 6-12 months and then reconsider getting cable. Then you aren't just forcing the decision on them and hopefully they appreciate the savings and get used to the alternative viewing methods. Worst case, in 6 months you get a good deal from the cable company to come back and at least you saved some money.
The local library and RedBox are good alternatives too. I find that paying for movies from Redbox is cheaper than paying for movies from Netflix as I don't watch enough, and there is enough free content on the internet/air. Redbox also offers a monthly DVD/Streaming plan in direct competition to Netflix.
I have to say, the only content you can't easily watch without cable is national news. I personally don't watch a lot of national news (I read it) so I could be wrong.