Changing algorithms during encryption Inspired by "Guarding against cryptanalytic breakthroughs: combining multiple hash functions", I am curious if there is a cryptographic reason to use only one algorithm during encryption.

For example, start with Blowfish, move to AES, switch to DES, etc, in a defined, but semi-unpredictable fashion (maybe basing which one to choose next off the last 4 bits of the most-recently-encrypted block's original plantext).

Would changing algorithm (but keeping the key identical, for sake of argument) have any cryptographic value? Could such a scheme be more resilient to cryptanalysis?
As many of the other answers have said the proposed method above is only as strong as the weakest cipher used (this is especially dangerous if the same key is used for all the ciphers).

Furthermore, basing the cipher transitions on the plaintext opens up the door to a range of timing side-channel attacks if any of the ciphers are faster or slower that each other.

One way you could guard against cryptanalytic breakthroughs is to use secret sharing to split a message $m$ into $n$ plaintexts ($p_i$) that must be combined to recover the original message. 
$$ m = p_0 \oplus p1 ... \oplus p_n $$
These $n$ plaintexts could then be enciphered by $n$ ciphers.

$$ciphertext = cipher_0(key_0, p_0)|cipher_1(key_1, p_1) ... |cipher_n(key_n, p_n)$$

The size of the ciphertext increases with the number of ciphers (size of message $\times n$), but you could ensure that even if $n-1$ of the ciphers were broken the message would remain secret. This also requires $n$ keys.

One could try some sort of key expander to expand a $key$ to a different key for each cipher:

$$key_0 = cipher_0(cipher_1( ... cipher_n(key, key)), cipher_1( ... cipher_n(key, key)))$$
$$key_1 = cipher_n(cipher_0( ... cipher_{n-1}(key, key)), cipher_0( ... cipher_{n-1}(key, key)))$$

but I don't have much faith its security (theoretically it is probably as weak as it's weakest cipher) and when one is so concerned with cryptanalytic breakthrough it would be foolish to introduce a "trusted" key expander (why not then introduce a trusted cipher and use that). I have asked the key expander issue as a separate question ( Designing a key expander out of ciphers ).