Springback Pasture adn Magosi the Waterveil are both lands I feel are underused. Chumping with a goat is often overlooked and taking your turns when you want is a good way to make some crazy, unbeatable plays
I define a utility land as a land that produces less mana than a basic land (either from coming into play tapped or providing colorless) but provides an additional ability that might be helpful. So this means Academy Ruins and Wasteland are utility lands, but Cabal Coffers and Urborg are not.
My decks have access to a perfect mana base, but that's not the only thing to keep in mind. You also must consider how badly your deck needs basic lands. I currently have four decks, for example, and only one of them runs strip mine:
The problem with defining [EDH] by what is "fun" is that everyone seems to define fun as what they don't lose to. If you keep losing to easily answered cards, that means you should improve your deck. If you don't want to improve your deck, then you should come to peace with the idea that you are going to lose because you chose to not interact with better strategies.
In mono colour decks, obviously, it is more leeway for adding more nonbasic lands though personally, I have lots of incentive to play nonbasic lands myself.
Basic lands are cheaper (okay, not a reason that you're looking for so lets move to the next reason)
Most nonbasic lands are really not as elegant. Basic lands usually comes into play untapped, produces coloured mana and does not deal damage to you when tapped.
My green deck runs Rofellos, Llanowar Emissary. While it is true that I don't always start with it in my starting hand but I do have quite a few ways of tutoring for it and when Rofellos do appear, sometimes, it matters. As for my Azami, Lady of Scrolls, I play the High Tide-Palinchron combo which is incentive enough for me to minimise nonbasics unless they are really, really necessary and not just good in circumstances X
Redundancy Card Advantage. This is mainly done by my green deck. Wasteland and most other nonbasic land hates are de facto dead cards given that the only nonbasic I run is a singleton Strip Mine.
The manabase in my Rith token deck is almost entirely basic to take advantage of Perilous Forays (I know this doesn't need basic lands, just land types) and Earthcraft. Green can cover for a lot of fixing that you would normally get from nonbasics, and the deck isn't looking for much utility from its lands.
There are lots of utility lands to support your strategies, and I'd recommend playing as many as you can as long as your deck can support them. And try to keep them on theme/synergic with the rest of your deck
Tower of the Magistrate goes in every 1-2 colored deck I have. Giving your opponents' creates "Pro-Equipment is just rude... I can't say I have ever used it on my own guys, but I suppose if someone was to take control of my equipped guy I would. After that it depends on the deck.