Time Capsule cryptography? Does there exist any cryptographic algorithm which encrypts data in such a way that it can only be decrypted after a certain period of time?

The only idea that I can think of, is something like this: Seed a PRNG with a public value. Run the PRNG for a week and use the final value it produces to encrypt the message. Now anyone who runs that PRNG for a week starting from the seed value you made public can decrypt the message. Obviously this breaks down since they could use more computational power than you; if the time span was years then Moore's Law would apply, etc.

Is there anything like this other than physically burying a private key on a USB stick in a literal time capsule?
Yes.

There has been a lot of work on "proof of work" protocols or "time-lock puzzles." Typically in cryptography, functions are either easy to compute or intractable. These protocols look at functions that are moderately hard to compute.

To do time-release encryption, you need a puzzle with the following properties:


Difficulty of the puzzle can be monotonically increased according to some difficulty parameter
Best algorithm to solve it is intrinsically sequential (parallel computing doesn't help)
Amortized cost of solving a group of puzzles is the same as a single puzzle
There is a trapdoor (shortcut) that allows efficient evaluation of the puzzle


With time-release crypto, the idea is to generate a puzzle that will take a certain amount of time to solve based on an estimate of a person's computational power and how it will grow in the future (e.g., Moore's law). As you can tell, it only gives you a fuzzy indication of how long it will stay secret (see below for a real world example). Property 2 is very important because adding parallel computation is easy and it is hard to estimate how much parallelization is possible.

Note that most proof of work protocols do not care about property 2 because they are used in different ways. These might be based on finding partial collisions/preimages in hash functions or exhaustive search of a small space (e.g., bitcoin), however speedups with parallel computing is trivial in these examples. There are also a number of memory-based puzzles that require lots (more than can be cached) of memory accesses, which is a more predictable measure of time on computers. 

Back to time-release crypto. The idea is to instantiate a puzzle $p$ with difficulty $d$: $p=\mathsf{Puzzle}(d)$. A trapdoor $t$ for efficiently solving it is known to the person who generates the puzzle. This person then encrypts her message under key $k$ with a normal encryption function: $c_1=\mathsf{Enc}_k(m)$. She then release an "encryption" of the key she used by combining the key with the solution to the puzzle. Note that she can efficiently solve the puzzle with trapdoor $t$ but the recipient can't. She computes: $c_2=k \oplus \mathsf{Solve}_t(p)$. The ciphertext is $c_1,c_2$ plus a description of the puzzle. 

To decrypt, the recipient computes $s=\mathsf{Solve}(p)$, which should take a moderate amount of time. He then recovers the key by $k=c_2\oplus s$, and can then decrypt $c_1$.

The disadvantage to time-release cryptography is that the recipient must devote an entire processor to solving the problem for the period of time that it should remain secret. 

The best proposal for a Puzzle with the right properties is due to Rivest, Shamir and Wagner in this paper. It is based on repeated squaring in RSA groups. A recent result precludes any intrinsically sequential time-lock puzzles in the random oracle model (e.g., based on hashing). 

In 1999, Rivest created a time capsule message to commemorate the 35th anniversary of MIT's Laboratory for Computer Science. He talks about how he designed it to require 35 years to decrypt. It is an interesting read.