Pyramids of Mars, The Doctor's Wife, The Caves of Androzani, The Waters of Mars and Vincent and the Doctor are common answers when you ask fans what their favorite story is from Doctor Who. But there are some stories which you'll only here one or two people say is their favorite, such as the 5 I'll talk about in this blog post. The episodes which deserve so much more recognition then they get.
The penultimate story for the beloved Ninth Doctor has the return of Blon Fel-Fotch Passameer-Day Slitheen and Mickey Smith, both of whom were last seen in "Aliens of London/World War Three". This episode is vital to NuWho mythology. It establishes the Rift, which is a device that Russel T. Davies returns to multiple times in his era. (But oddly enough, Moffat hasn't used it at all.) The episode has character development for all main characters, specifically Rose and Mickey.
The episode also acts as a prequel of sorts to Torchwood and Bad Wolf/The Parting of the Ways. But the episode isn't just good because of that. The acting and dialogue is top-notch, and the dinner scene between the Doctor and Blon Fel-Fotch is one of the true highlights of Series 1. In short, Boom Town is an episode that is incredibly important to the Russel T Davies era, and is a hidden gem.
The Happiness Patrol
The Happiness Patrol is one of my favorite stories. It's quite possibly in my top 5. It's cruelly underrated and deserves so much more praise then it gets. Yes, it has the Kandyman. But the Kandyman himself is a fascinating individual. He doesn't want to kill really, he just wants to experiment. Helen A, the true villain of the piece, is an amazing character. The whole story is an onion, with many layers to it. The performances are excellent, the moody tone works well and while there are weird aliens, it's still an amazing adventure which has one of the most interesting resolutions to a Doctor Who story.
The Beast Below
In Doctor Who Magazine Issue 433, Steven Moffat himself said that he "struggles to love The Beast Below". While it's not as good as the previous episode in the run, The Eleventh Hour, The Beast Below is an excellent "companion in the future for the very first time" episode. It's excellent character growth for Amy, as well as making us understand who she is. There's a sinister plot and some dark Doctor (As always, there is an excellent performance from Matt Smith.) and while there's some awful dialogue ("Has he done the thing?") it's a wonderful one-off story.
The TV Movie
Often criticized for the "American-ized" story and only remembered because of Paul McGann's brilliant performance, the TV Movie has some excellent moments and touches which, in this writer's opinion, outweigh the cons. The TARDIS Console, the Seventh Doctor gets a proper ending, the acting from the lead characters and the callbacks to the classic series make you (somewhat) forget that Eric Roberts played the Master for one night only..
The Edge of Destruction
The third serial of Doctor Who is set entirely in the TARDIS and features only the main cast. Often overlooked as cheap and boring, this two-parter is the source for the warmth that grew between the original TARDIS crew. After being accused of sabotaging the ship by an injured Doctor, Barbara and Ian (the latter's in a bathrobe. Ooh la la indeed. ) stand up to the Doctor, and it's proof that #BarbaraWrightIsOneOfTheBestCompanions. (Get that trending twitter.) It's a creepy episode reminiscent of The Twilight Zone. It is arguably one of the greatest serials of the Hartnell Era, and it's a shame that it's overlooked by so many fans.
So those are my top 5 Underrated Doctor Who Stories. I'd highly recommend you to watch all, or rediscover the ones you've already seen. Feel free to comment below giving me feedback and your favorite underrated Doctor Who stories.