Let's say I want to hash some data, using SHA256, in order to prove I know something. ... However, there are a lot of other cases where the input is not as "bad".
Ask the following questions, but answer then at the worst case (from your point of view) that will exist between now and when in the future you predict you will no longer care at all about an attacker finding and/or publishing what you're hiding. In your case, "what you're hiding" may be your bitcoin wallet ID, etc.:
What is the value of an attacker finding out what you're hiding?
What is the largest keyspace an attacker would have to search withing to guess what you're hiding? I.e. brute force attack.
What is the smallest keyspace an attacker would have to search withing to guess what you're hiding? I.e. rules-based dictionary attacks, weaknesses in your hashing algorithms, not every bit is random, weaknesses in the RNG that helped with what you're hiding, weaknesses in other algorithms, etc.
Does PBKDF2 (or HMAC, which it includes) increase the smallest keyspace? Scrypt? Bcrypt?
What are the chances of a flaw being discovered that you don't know about now?
At what speed could a poorly funded attacker search said keyspaces (assume $5kish, so perhaps 8 top end GPU's or 10 very good CPU's - a teen with rich parents, a hobbyist, a StackExchange member). A moderately funded attacker? A well funded attacker? A megacorp or government?
What level of attacker do you care about?
How much extra CPU time/member for one of these techniques could you spend without inconveniencing you at all? Inconveniencing you only a little? Inconveniencing you moderately? Inconveniencing you a lot?
What is the chance of the technique you choose helping an attacker compared to the technique you were considering before? For instance, PBKDF2-HMAC-SHA-256 is no worse than SHA-256, since they share the same base hash, but the former has considerably more protection against certain types of attacks.
Take these answers and apply them to a cost-benefit risk analysis. Go with your answer.
For myself, I would at minimum use however many rounds of whichever of the three I like does not inconvenience me at all, and very likely more - I tend to think that 4-8 seconds of waiting isn't a problem when I, a human, am looking up secret information. Scale iterations up over time as you see fit.