Is there a length-preserving encryption scheme? Is there a length-preserving encryption scheme, that preserves the lengths of input sizes such that the length of the input plain text is same as length of the output cipher text ?
As @fgrieu mentioned, what you're after is FPE. The papers he linked deal with FPE on a very small domain, but it looks like you're interested in encrypting longer strings.

For that, you need a wide block cipher. Unlike traditional blockciphers, these typically allow different input lengths, which is a plus. They meet your criterion of not revealing shared prefixes/suffixes. Examples (any of which will be secure): EME, EME2, HCTR, HEH, TET, PEP. Tracking down a good implementation might be problematic; I don't know any off-hand. Some, including EME/EME2, are patented (but can be licenced under "reasonable, non-discriminatory" terms). Depending on the mode, they operate at roughly half the speed of standard encryption algorithms.

In terms of providing confidentiality, a result by Bellare and Rogaway ("Encode-then-encipher encryption: How to exploit nonces or redundancy in plaintexts for efficient cryptography") shows that you get it for free as long as you can guarantee that all plantexts are distinct (e.g., they already have distinct sequence numbers encoded into them somehow). The only information these ciphers leak is plaintext length, and whether or not a plaintext is repeated. 

You said authenticity was not a concern, but perhaps it's worth noting that you can get this fairly cheaply if the plaintext contains some type of redundancy that you check upon decryption.

Finally, these algorithms are tweakable ciphers, which means the take an additional input, called the tweak. You can use (meta)data from any accompanying headers as the tweak (or just used a fixed string). Again, if the tweak is distinct each time, then you have confidentiality even if a plaintext is repeated. But at that point it might be easier to, e.g., take a 64-bit nonce from the headers and use that as the high-order bits of a counter-mode IV.