One-Time Pad and Shamir's Secret Sharing are two examples of cryptographic algorithms, where some secret value is involved, and which are nonetheless immune to brute force, even against attackers with unlimited computing abilities. Their key feature is "lack of key redundancy": there is no way to filter out "bad" keys. This shows in the fact that OTP requires the secret key to be as long as the encrypted data, and for Shamir's Secret Sharing the total size of the "shares" is even longer than the shared data.
Probabilistically speaking, you get the same property from an AES encryption, as long as you encrypt a single block, and use a key larger than that (e.g. AES-256 for encrypting a single 128-bit data element). The idea is that for a given ciphertext, any plaintext can match (given C and P, there are quite a few keys K such that AESK(P) = C). Hence the attacker cannot choose the "right" plaintext, even if exploring the whole key space. Of course, reusing the same key for anything else, even encrypting another 128-bit block with AES, would give to the attacker all the redundancy he needs to filter out keys, making brute force viable again (for our hypothetical attacker with a computer bigger than a galaxy, that is).
Algorithms which resist brute force have limited applicability, precisely because of the need for very long keys. In practice, against attackers with earth-based technology, brute force attacks are thwarted by using "long enough" keys. If you consider than an attacker may muster enough computing power to perform 2n "elementary operations", then you use keys of at least n bits; if you fear quantum computers, you use 2n bits (for anything symmetric, like symmetric encryption or hashing, a quantum computer may theoretically explore a key space of size N with effort sqrt(N), but no better; hence, it suffices to use a twice larger key). Traditionally, we set n=80 but constant progress in technology availability is beginning to force us to bump that value a bit, if we want to keep a convincingly large security margin. Since powers of two are good, it is now customary to use n=128, although the actual limit for Mankind as a whole (in an improbable sci-fi scenario in which all humans cooperate and work for that goal) can be estimated to be somewhere between 90 and 100.
Asymmetric algorithms (asymmetric encryption, signatures...) are much weaker, in that there are known attacks which are much better than "brute force" -- and a quantum computer makes the attacks trivial, for most of them. But since this is not brute force anymore, it is out of scope of your question.