Cards in hand are options. Having more cards in hand gives you more options. Having the right cards in hand gives you better options.
Card filtering (of which scry cards are a subset) is good any time you want a specific card. Your intuition about combo decks is correct, but it doesn't stop there. Consider a control deck that uses a mixture of counterspells, spot removal, and board wipes, for instance: if your opponent's about to burn you out, you need a counter; if your opponent dropped a Titan or a planeswalker you'll want spot removal ASAP (and it has to be the right kind, too); if your opponent has two Dungrove Elders or an army of Spirit tokens beating you down you'll want that sweeper. Card filtering makes it easier to have all of those when you need them; this is especially valuable with very specific hosers you keep in your sideboard.
Card draw implicitly has all the same benefits as card filtering (since you're likewise digging faster through your deck) but also gives you card advantage. Card advantage almost always matters. Any time you're actually going to get to play most of your hand before the game ends, card advantage will make a difference; if you're playing against, say, a very fast red deck that just throws its resources away to try to kill you as quickly as possible, then the loss of tempo from casting a card-draw spell might not be worth the benefit of extra cards in hand.
There's a third class of cards it's worth thinking about in the same discussion: cards that search your whole deck, also known as "tutors". Card-filtering cards conceptually occupy a middle ground between pure card draw and tutors; they're appealing because many decks have several cards which can acceptably answer a problem, and being able to dig up an acceptable card cheaply and quickly is often regarded as more valuable than finding just the right card at too high a cost or a turn too late.
The main price of all these advantages is tempo. Any time you're spending a turn's mana on something that doesn't immediately affect the board state, you're potentially losing ground to your opponent(s). Hand-sculpting is all about giving up something now to get a better hand for next turn. The decks that use it best are either those that can devalue tempo (using control techniques) or those that are willing to throw everything away to improve their next turn. That said, any time a duel comes down to attrition of cards in hand, card draw can power you through a finish -- every deck wants card draw as long as it can afford to pay the price (which is why, in its day, Skullclamp was all over aggro decks).
When weighing the value of different get-more-cards cards, pay attention to spell types and casting costs. Reactive decks are much better off with Instant-speed card draw/filtering, because being able to play your hand-sculpting cards on your opponent's end step allows you to keep mana open for responses during your opponent's turn. You also want spells that fit nicely into your mana curve -- ideally, ones you can cast before you'd be casting whatever it is you'd usually dig for, so they're not slowing you down. It's reasonable to run a few big splashy high-cost card draw cards to help you lock up the late game (Consecrated Sphinx or Blue Sun's Zenith, for instance), but card filtering is generally best on little cards you can use early to find what you need.
The other thing you should be on the lookout for is hand-sculpting cards with convenient side-effects. Forbidden Alchemy, for instance, dumps three cards into your graveyard -- to some decks, that's like three extra cards in hand. Brainstorm is a powerhouse in any Legacy deck that plays blue, but also powers up cards that interact with the top card of your library, like Counterbalance or Delver of Secrets. Preordain not only allowed Pyromancer Ascension decks to search for cards to trigger their combo but also served as a worthwhile trigger itself. Tezzeret's Gambit is choice card draw for decks obsessed with +1/+1 counters, poison counters, or planeswalker loyalty counters.