user78: This question asks about how to work with bitcoin via an API without requiring a local blockchain. The only answer is about blockchain.info's JSON API, but it appears that unlike the web version of blockchain.info, the JSON API requires the account passwords to be sent to the server.
Is there another remote API that allows one to perform various bitcoin operations without compromising security - without sending private keys anywhere, but rather signing transactions locally? The API should not require any downloads - SPV does not fall under this category - but should just be a remote API to the bitcoin network that doesn't require any state / bootstrap from its client.
If I recall correctly then Stratum was supposed to be this API. Did it ever take off?

user3347: bitcore-wallet-service by Bitpay seems to satisfy your conditions, in that it does not require you to log in or send the private key.

user78: There are quite a few answers in the bitcointalk thread. This is what I consider to be the best option:

Using blockchain.info for queries
Using bitcoinj to sign transactions
Using blockchain.info broadcast API to broadcast transactions

This class from the the android version of My Wallet is supposed to implement this scheme.

user77551: 
There is a simple and customized Git repo available (Node.js).

Github Repository Link
This code allows you to do things such as: 

balance - Retrieves the balance of a wallet. 
fees - Gets a list of
current fees based on the BitCoin network going rate. 
utxo - Pull a
list of unspent transaction outputs. 
pushtx - Push a raw transaction
onto the blockchain.


user5522: The BOP Enterprise Bitcoin Server is an open source full node implementation with remote (that is client side) wallet. The server downloads the block chain does the transaction and block validation and routes transactions signed at the client.
The client connects to the server via a message bus. There is a Java and other APIs available with added client side features. Source code: https://github.com/bitsofproof/supernode
Commercial support and hosted instances available at http://bitsofproof.com

78: <p><a href="https://bitcoin.stackexchange.com/questions/2333/is-there-a-remote-bitcoin-api-that-doesnt-require-anything-to-be-stored-locally">This question</a> asks about how to work with bitcoin via an API without requiring a local blockchain. <a href="https://bitcoin.stackexchange.com/a/3991/78">The only answer</a> is about blockchain.info's JSON API, but it appears that unlike the web version of blockchain.info, the JSON API requires the account passwords to be sent to the server.</p>

<p>Is there another remote API that allows one to perform various bitcoin operations without compromising security - without sending private keys anywhere, but rather signing transactions locally? The API should not require any downloads - SPV does not fall under this category - but should just be a remote API to the bitcoin network that doesn't require any state / bootstrap from its client.</p>

<p>If I recall correctly then Stratum was supposed to be this API. Did it ever take off?</p>
 3347: <p><a href="https://github.com/bitpay/bitcore-wallet-service#security-considerations" rel="nofollow">bitcore-wallet-service</a> by Bitpay seems to satisfy your conditions, in that it does not require you to log in or send the private key.</p>
 78: <p>There are quite a few answers in the <a href="https://bitcointalk.org/index.php?topic=144347.0" rel="nofollow noreferrer">bitcointalk thread</a>. This is what I consider to be the best option:</p>

<ol>
<li>Using blockchain.info for queries</li>
<li><a href="https://bitcoin.stackexchange.com/questions/7708/how-do-i-create-an-offline-transaction-in-java-to-broadcast-via-blockchain-info">Using bitcoinj to sign transactions</a></li>
<li>Using blockchain.info broadcast API to broadcast transactions</li>
</ol>

<p><a href="https://github.com/blockchain/My-Wallet-Android/blob/master/src/piuk/MyRemoteWallet.java" rel="nofollow noreferrer">This class</a> from the the android version of My Wallet is supposed to implement this scheme.</p>
 77551: <blockquote>
  <p><strong>There is a simple and customized Git repo available (Node.js).</strong></p>
</blockquote>

<p><a href="https://github.com/Blank101/bitcoin-transaction" rel="nofollow noreferrer">Github Repository Link</a></p>

<p>This code allows you to do things such as: </p>

<ul>
<li>balance - Retrieves the balance of a wallet. </li>
<li>fees - Gets a list of
current fees based on the BitCoin network going rate. </li>
<li>utxo - Pull a
list of unspent transaction outputs. </li>
<li>pushtx - Push a raw transaction
onto the blockchain.</li>
</ul>
 5522: <p>The BOP Enterprise Bitcoin Server is an open source full node implementation with remote (that is client side) wallet. The server downloads the block chain does the transaction and block validation and routes transactions signed at the client.</p>

<p>The client connects to the server via a message bus. There is a Java and other APIs available with added client side features. Source code: <a href="https://github.com/bitsofproof/supernode" rel="noreferrer">https://github.com/bitsofproof/supernode</a></p>

<p>Commercial support and hosted instances available at <a href="http://bitsofproof.com" rel="noreferrer">http://bitsofproof.com</a></p>
