As 2012 ebbs away and 2013 looms large, it’s time to consider the state of prime-time television and needed fixes to favorite shows.

But it’s not just the networks and their series that need to make New Year’s resolutions: Viewers also need to reconsider spending some time with the best shows they’re not watching.

For networks

•Fox’s “Glee” (9 p.m. Thursdays) needs to cut its original cast members loose. They’ve proved enjoyable over the years, but the show’s efforts to keep them around smack of illogical desperation.

Does anyone really buy Finn (Cory Monteith) as a temporary glee club sponsor? Or that so many characters that graduated in May would come home from college to participate in high school productions?

An occasional return – like for the episode set over Thanksgiving – is fine but beyond that, “Glee” needs to move on. The new characters are sufficient replacements and when the show stays focused on the kids in high school, it’s fine – not great (the show’s best episodes are in its past) but certainly watchable.

•Now that ABC’s “Revenge” (9 p.m. Sundays) has gone the way of “Alias” with a plot involving a conspiracy-minded organization (“the Initiative”), it’s become convoluted and a lot less fun. The show still has its moments, but seems to have lost touch with its initial “Count of Monte Cristo” inspiration and spun off into cuckoo soap territory. It needs to return to its roots.

New episodes of “Revenge” resume Jan. 6, but then it will be a choice between it and “Downton Abbey,” a far superior soap in every way.

•As much as I loved “Homeland” (returning in the fall on Showtime) in its first season, the show rocketed off the rails in Season 2 with too many unbelievable plot twists that brought to mind “24.” Not that there’s anything wrong with “24,” but in its first year “Homeland” was more grounded, less pulpy. That’s no longer true.

•Then there’s FX, now home to two of the most sadistic shows on TV, “Sons of Anarchy” and “American Horror Story” (“Sons” returns with new episodes in the fall; “AHS” finishes its second season with four episodes that began airing this week at 10 p.m. Wednesdays).

“Sons,” in particular, is a smart, well-written drama but it is so, so brutal. This season, one character ended up with a face full of nails and another saw his daughter set on fire and killed in front of him. Being edgy is fine, but the cruelty on display got to me.

The same goes for “American Horror Story,” which turned me off with its murderous Santa (Ian McShane, “Deadwood”) in what passed for a Christmas episode this month. Sure, it’s a horror show set in an asylum, but those scenes of premeditated mayhem outside Briarcliff Manor were more upsetting to watch than anything else this season.

For viewers

And now for the TV shows that are working quite well but don’t have enough viewers (aka “the best shows you’re not watching,” but you should try to catch).

•Any episode now, ABC’s “The Neighbors” (8:30 p.m. Wednesdays) may implode, but until it does, it’s a TV comedy worth defending. Yes, many critics hated it but the vitriol was wholly undeserved.

The show is a bit wacky in its premise – human family moves in next door to extraterrestrial neighbors – but it’s a perfect show for parent-child co-viewing with enough layers that both generations are entertained.

•Fans of soaps (I’m looking at you, disappointed “Revenge” viewers) should give ABC’s “Nashville” (10 p.m. Wednesdays) a shot. And, no, you don’t have to be a fan of country music to enjoy the “All About Eve”-style plots revolving around up-and-coming singer Juliette Barnes (Hayden Panettiere, “Heroes”) and veteran Rayna Jaymes (Connie Britton, “Friday Night Lights”). It isn’t groundbreaking TV, but it’s a thoroughly enjoyable soap for fans of the genre.

•Similarly, ABC Family’s “Bunheads” (9 p.m. Mondays beginning Jan. 7) is an enjoyably witty, soapy show from the writer of “Gilmore Girls.” It’s yet to reach the creative heights of “Gilmore,” but this story of a dance teacher (Kelly Bishop from “Gilmore Girls”) and her daughter-in-law (Sutton Foster) running a dance studio in a small town is a delight for fans of gentler, serialized storytelling.

•“AHS” executive producer Ryan Murphy has the same credit on NBC’s “The New Normal” (9:30 p.m. Tuesdays), a wildly uneven comedy. The story of a gay couple and the woman surrogate carrying their child can occasionally be strident in the worthy defense of gay rights. And attempts to write conservative characters either sound like mad (but often hilarious) ravings, or like liberals trying to write conservatively. But the lead characters are often entertaining as is the surrogate’s bespectacled daughter in this sitcom that mixes outrageous humor with heart.

•Fans of cop shows who haven’t watched TNT’s “Southland” (10 p.m. Wednesdays beginning Feb. 13) are missing out on the best police show currently on TV. A gritty, character-based drama, last season “Southland” offered a strong dramatic platform for Lucy Liu, who’s now starring on “Elementary.”

But it’s the show’s regulars – Ben McKenzie, Michael Cudlitz, Shawn Hatosy, Regina King – and sharp writing that make trips to L.A.’s seamy, underbelly worthwhile.