Spent to Cast: Ruminations

"Spent to Cast," aka Ogre Savant Ability, aka Sunburst, aka cards in the Shadowmoor/Eventide cycles including River's Grasp and Moonhold.  These cards care about the mana that was spent to cast them. Sunburst doesn't care what mana was spent so long as it's different and it provides one of two set effects related to that. That makes it different enough that it discussed in depth elsewhere.

Spent to Cast encourages splashing other colors. It usually requires mana of one color to cast, but gives a bonus if another color is spent. It's popular on instants and sorceries and when it's used on creatures, it often confers a one-time effect , even if that effect is just to keep the creature, in the case of the Simic, Azorious, and Rakdos implementations (where Spent to Cast acts like strange Evoke instead of a strange Kicker). This avoids memory issues in much the same way that Sunburst does with counters.

Cons

The spell taped to a creature issue sometimes results in cross-color abilities: Court Hussar has a very blue ETB effect, but has a white ability, one you only get to use if you pay white mana for it. While it's an interesting approach, it ends up being a blue card with vigilance, just like Azorius Herald is an unblockable white card and Crypt Champion is a black card with Double Strike. That particular approach to the color pie might not work in a core set.

Crypt Champion itself raises an interesting point; while Crypt Champions can't reanimate one another, these strange evoke creatures are very resistant to being cheated into play. This might discourage new players and even cause uncertainty when the appropriately colored mana is spent on an ability that puts them into play (Quicksilver Amulet or Birthing Pod). This is either an opportunity for education or a dangerous point of confusion.

New players may want to maximize their use of these cards by holding on to them until they can pay both costs. If you're paying 5 mana for a 3/2, it's not unreasonable to want to wait until you can get it with the Unsummon attached.

The creatures with these abilities usually have ETB effects. With the conditional triggers, that often leaves very little room for flavor text.

The Shadowmoor/Eventide cards use hybrid mana, the drawbacks of which have been noted and are especially problematic in a core set.

Some intermediate players might wonder if a card like Cankerous Thirst needs (one creature on the battlefield) or can have(Illusions) a second target to cast, even if only one color of mana is being used to play it. As a card that sometimes acts as a counterspell, Repel Intruders sidesteps a number of similar problems with the classic "up to" wording.

These cards start at 1C for cost, unless they're artifacts or hybrid. If they're hybrid, they're modal to some degree.

Scry was mostly blue in 2011 and Bloodthirst was red, black, and green in 2012. A color sensitive mechanic doesn't fit so well into that kind of pigeonhole. If it's a cycle, then we get it in increments of 5 cards, which would narrow implementations to 5, 10, or 15 cards.

Pros

Cards like Batwing Brume and Invert the Skies can give new players a way to understand the sections of the color pie; White likes defense, Black likes to punish, Blue likes flying, Green doesn't like flying, etc. They can also get new players to appreciate other colors that they might not usually like (A new player with an affinity for white and antipathy for black black might swing a Swamp, just in case, for Batwing Brume and find they like it.). Probably no enemy color pairing in a core set, and definitely no hybrid mana costs, but it's an option.

They're low on secondary color commitment, so they're optimal for splashing.

Their implementation as minor, color-based effects means that they are open in how they can manifest and in how they can be supported.

Variations on the Theme

Obviously, you don't get to play with the ability much beyond the basics in a core set. These ideas are just there to expand on the idea and to demonstrate some of the versatility the ability has, giving good reasons to put the foundations in a core set. These are not ideas or submissions for M13, but potential the design presents.
 
Multiple Colors: A card of one color with two distinct abilities based on other colors or an "OR" condition like the card below.

On other cards:

Dies triggers: Instead of having an ability whenever they enter the battlefield, if a particular payment was made to cast that creature, it could enter the battlefield with a counter on it. When it dies, if it has that counter on it, you get another effect.

Other Costs: Other costs don't quite grow on trees. While it'd be great for a set that overlaps with one featuring Phyrexian Mana, Evoke, or even Forecast, a few enablers would have be used.

Artifacts & Colorless Mana: Then, of course, there's a requirement to spend colorless mana.