Because generating mana of any color is so powerful and because lands are so cheap, the drawbacks and conditions for those types of lands are widely varied and quite unpredictable. Almost wild, really.
In each Magic game, you have a total amount of mana you generate between each of your untap steps. If there's a land that isn't tapped when you start your turn, it's wasted potential (mostly). The goal is to have a progression of mana that you've used every turn until you've won. If you stall at four lands, that total for the first five turns looks like 1+2+3+4+4. By that fifth turn, your first land has given you five mana.
If you have Undiscovered Paradise in your hand, you're going to have to decide at some point whether to play a land that's going to churn out mana every turn or play UP again to cast a spell now and face the same dilemma next turn. Undiscovered Paradise doesn't cost you one land drop or one mana, but one mana every turn you have to replay it. If you tap it for a color of mana you can already produce, it's even more futile.
That's not saying I don't like it or that it's unplayable—I love all of these crazy lands because they're crazy and I'm certainly not qualified to say what's "playable" and what isn't—what I'm saying is that the cost is deceptively high. Of course, you're getting a mana of any color, so maybe it's worth it.
Not being around is a pretty common tradeoff for these kinds of versatile lands. Thran Quarry and Glimmervoid sacrifice themselves if you don't control a creature or artifact, respectively. Gemstone Mine does this too, but where it's more "used up," these two guys just need you to satisfy another condition to stay around. Especially if you gamble by playing them first turn, you stand to lose a lot of gas, long-term.
What about cards in your hand? Forsaken City requires that you exile a card from your hand to untap it. While you can choose whether or not to pay the cost, you have to do so before the turn-defining draw step. Forsaken City seems like a card that demands a really good player to get the most out of it. While taking some damage or losing land is a high price, that price is usually just as damaging in one deck as another. Choosing when to pitch a card and which one are a tougher, swingier series of choices.
Speaking of cards that damage you, City of Brass' popularity tells us clearly that one damage is worth less than one mana of any color. The popularity of Tarnished Citadel tells us that tripling that price is not. When Grand Coliseum tweaked City of Brass by coming onto the battlefield tapped and adding the ability to produce colorless mana as well, it seemed like a good compromise.
Coming onto the battlefield tapped is just code for "tap this land to pay for itself." Rupture Spire takes it a turn further by actually making you pay another mana on top of that. It and Transguild Promenade (a functional reprint) the only lands I know of that cost two mana to play.
In the world of Magic, time is mana. Mirrodin's Core turns time (and its own colorless mana) into mana of any color. That's a worst-case-scenario though. In reality, you can keep it open, charge it up during an opponent's end step and use the mana if you have to during your next turn. In terms of drawbacks, I think Mirrodin's core is both the most complex and the most balanced. That's probably not a coincidence.
Rhystic Cave is my favorite because it's weird. It allows opponents to pay mana to keep you from adding mana to your mana pool. It's highly interactive and I think it's the only one on this list that lets your opponent control whether it works or not, which creates really cool rules stuff that I like. My only real doubts come from the fact that the guys on Gatherer agree with me.
Anyway, this is running way too long, so stand by for the second half of the last part of this gripping series next week.