Neo4J Rest Javascript wrapper
Interesting question,

The most striking thing is your repeated use of this pattern:

connection.sanitizeId(response['xxx']);


I dont believe sanitizeId should be a function of connection. Also, response is not a good name because it often is part of a response from the query and not the actual response. And, it is suggested that response.xxx makes more sense than response['xxx']. To that end, I feel that sanitizeId should be part of the response or data. Also, I would be tempted to call it simply sanitize.

function addSanitizer( data , server){
  data.sanitize = function( propertyName ){
    return this[propertyName].replace( server , "" );
  }
  return data;
}


Then you could do

function Node(response) {
    this.id   = response.sanitize( 'self' );
    this.data = response.data;
}


Or, if you agree that response might be misleading

function Node(node) {
    this.id   = node.sanitize( 'self' );
    this.data = node.data;  
}


Node with be called like this:

getNode: function (id, callback) {
    var connection = this;
    get(this.server + id + "/properties", function (data) {
        if (data == null) data = {data: {}};
        else data = {data: data};
        data['self'] = id;
        callback(new Node(this.addSanitizer( data, this.server ), data));
    });
},


From a style point:


You are skipping new lines on your if statements: if (data == null) data = {data: {}};, dont do that
Your code stretches quite a bit horizontally, but not too bad, feel free to to split up some of your longer lines into something more readable, this :

createRelation: function (start, target, type, callback) {
    var connection = this;
    post(this.server + start + '/relationships', {to: this.server + target, type: type}, function (data) {
        callback(new Relation(connection, data));
    });
}


could be 

createRelation: function (start, target, type, callback) {
    var connection = this,
        data = {to: this.server + target, type: type};
    post(this.server + start + '/relationships', data , function (data){
        callback(new Relation(connection, data));
    });
}



The code looks all in all fine to me. For a Java developer you did good :P