wifi web server that doesn't slow down a robot?

Server plus one ping sensor has been tested using the newping library to be successful. 29ms millis timer on the ping.

That is a good start. You may be running out of memory. You need to try using the F() macro on any static text strings in your code. Below is some server code that uses the F() macro to save memory so you can see how to encapsulate the text strings.

// zoomkat's meta refresh data frame test page 8/17/13
// use http://192.168.1.102:84 in your brouser for main page
// http://192.168.1.102:84/data static data page
// http://192.168.1.102:84/datastart meta refresh data page
// for use with W5100 based ethernet shields
// set the refresh rate to 0 for fastest update
// use STOP for single data updates

#include <SPI.h>
#include <Ethernet.h>

const int analogInPin0 = A0;
const int analogInPin1 = A1;
const int analogInPin2 = A2;
const int analogInPin3 = A3;
const int analogInPin4 = A4;
const int analogInPin5 = A5;

byte mac[] = { 0xDE, 0xAD, 0xBE, 0xEF, 0xFE, 0xED }; //physical mac address
byte ip[] = { 192, 168, 1, 102 }; // arduino ip in lan
byte gateway[] = { 192, 168, 1, 1 }; // internet access via router
byte subnet[] = { 255, 255, 255, 0 }; //subnet mask
EthernetServer server(84); //server port
unsigned long int x=0; //set refresh counter to 0
String readString; 

//////////////////////

void setup(){
  Serial.begin(9600);
    // disable SD SPI if memory card in the uSD slot
  pinMode(4,OUTPUT);
  digitalWrite(4,HIGH);

  Ethernet.begin(mac, ip, gateway, gateway, subnet);
  server.begin();
  Serial.println(F("meta refresh data frame test 8/17/13")); // so I can keep track of what is loaded
}

void loop(){
  EthernetClient client = server.available();
  if (client) {
    while (client.connected()) {
      if (client.available()) {
        char c = client.read();
         if (readString.length() < 100) {
          readString += c; 
         } 
        //check if HTTP request has ended
        if (c == '\n') {

          //check get atring received
          Serial.println(readString);

          //output HTML data header
          //client.println("HTTP/1.1 200 OK");
          //client.println("Content-Type: text/html");
          //client.println();
          
          client.print(F("HTTP/1.0 200 OK\r\nContent-Type: text/html\r\n\r\n"));

          //generate data page
          if(readString.indexOf("data") >0) {  //checks for "data" page
            x=x+1; //page upload counter
            client.print(F("<HTML><HEAD>"));
            //meta-refresh page every 1 seconds if "datastart" page
            if(readString.indexOf("datastart") >0) client.print(F("<meta http-equiv='refresh' content='1'>")); 
            //meta-refresh 0 for fast data
            if(readString.indexOf("datafast") >0) client.print(F("<meta http-equiv='refresh' content='0'>")); 
            client.print(F("<title>Zoomkat's meta-refresh test</title></head><BODY>
"));
            client.print(F("page refresh number: "));
            client.print(x); //current refresh count
            client.print(F("

"));
            
              //output the value of each analog input pin
            client.print(F("analog input0 is: "));
            client.print(analogRead(analogInPin0));
            
            client.print(F("
analog input1 is: "));
            client.print(analogRead(analogInPin1));
                        
            client.print(F("
analog input2 is: "));
            client.print(analogRead(analogInPin2));
            
            client.print(F("
analog input3 is: "));
            client.print(analogRead(analogInPin3));
                                    
            client.print(F("
analog input4 is: "));
            client.print(analogRead(analogInPin4));
            
            client.print(F("
analog input5 is: "));
            client.print(analogRead(analogInPin5));
            client.print(F("
</BODY></HTML>"));
           }
          //generate main page with iframe
          else
          {
            client.print(F("<HTML><HEAD><TITLE>Zoomkat's frame refresh test</TITLE></HEAD>"
            "Zoomkat's Arduino frame meta refresh test 8/17/13"
            "

Arduino analog input data frame:
"
            "&nbsp;&nbsp;<a href='/datastart' target='DataBox' title=''yy''>META-REFRESH</a>"
            "&nbsp;&nbsp;&nbsp;&nbsp;<a href='/data' target='DataBox' title=''xx''>SINGLE-STOP</a>"
            "&nbsp;&nbsp;&nbsp;&nbsp;<a href='/datafast' target='DataBox' title=''zz''>FAST-DATA</a>
"
            "<iframe src='/data' width='350' height='250' name='DataBox'>"
            "</iframe>
</HTML>"));
          }
          delay(1);
          //stopping client
          client.stop();
          //clearing string for next read
          readString="";
        }
      }
    }
  }
}