What encryption should I use: Blowfish, Twofish, or Threefish? The title of this thread pretty much sums up what I'm asking: what is the best encryption to use out of the three — Blowfish, Twofish, or Threefish?
TL;DR: Twofish and Threefish are fine.
It is not the best idea to have the cipher you want to use hardcoded because you can't upgrade easily when one of them is broken. to quote mikeazo in the comments:

What you should do is develop your application to not be bound to a specific cipher.

Twofish

In 1999, Niels Ferguson published an impossible differential attack that breaks six rounds out of 16 of the 256-bit key version using $2^{256}$ steps.


As of 2000, the best published cryptanalysis on the Twofish block cipher is a truncated differential cryptanalysis of the full 16-round version. The paper claims that the probability of truncated differentials is $2^{−57.3}$ per block and that it will take roughly $2^{51}$ chosen plaintexts (32 petabytes worth of data) to find a good pair of truncated differentials.


Bruce Schneier responds in a 2005 blog entry that this paper does not present a full cryptanalytic attack, but only some hypothesized differential characteristics: &quot;But even from a theoretical perspective, Twofish isn't even remotely broken. There have been no extensions to these results since they were published in 2000.&quot;

https://www.schneier.com/academic/twofish/
https://www.schneier.com/blog/archives/2005/11/twofish_cryptan.html
Threefish

In October 2010, an attack that combines rotational cryptanalysis with the rebound attack was published. The attack mounts a known-key distinguisher against 53 of 72 rounds in Threefish-256, and 57 of 72 rounds in Threefish-512. It also affects the Skein hash function. This is a follow-up to the earlier attack published in February, which breaks 39 and 42 rounds respectively. In response to this attack, the Skein team tweaked the rotation constants used in Threefish and thereby the key schedule constants for round 3 of the NIST hash function competition.


In 2009, a related key boomerang attack against a reduced round Threefish version was published. For the 32-round version, the time complexity is $2^{226}$ and the memory complexity is $2^{12}$ for the 33-round version, the time complexity is $2^{352.17}$ with a negligible memory usage. The attacks also work against the tweaked version of Threefish: for the 32-round version, the time complexity is $2^{222}$ and the memory complexity is $2^{12}$ for the 33-round version, the time complexity is $2^{355.5}$ with a negligible memory usage.

http://www.skein-hash.info/ (the design of Threefish is based on it).
Blowfish

At this point, though, I'm amazed it's still being used. If people ask, I recommend Twofish instead.
— Bruce Schneier, Blowfish's creator, 2007

Swordfish
                         GABRIEL
              Here's the deal. I need a worm,
              Stanley. A hydra, actually. A
              multi-headed worm to break an
              encryption and then sniff out
              latent digital footprints
              throughout an encrypted network.

                            STANLEY
              What kind of cypher?

                            GABRIEL
              Vernam encryption.

                            STANLEY
              A Vernam's impossible. Its key
              code is destroyed upon
              implementation. Not to mention
              being a true 128 bit encryption.

                            GABRIEL
              Actually, we're talking 512 bit.

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