I'm not sure what type of ultrasonic sensor you are planning on, but the Maxbotix sensors have the capability to be daisychained to sequence the triggering for this very reason. I recommend you read section 6 here: http://www.maxbotix.com/MaxSonar-EZ1__FAQ.html
I am using the 6f technique on my Charlie bot.
This wouldn't occur if you did the pings at different times though as the initial ping is started by the pulseout and not a continuous ping. This of course would be for sensors that have a trigger/response method of getting distance and wouldn't work with ultrasonic sensors that give continuous analoge readings.
If you do a ping simulataneously, then yeah, you could run into issues as zeitron mentioned.
With IR sensors, you'd run into an issue more as they usually have continuous ir emmisions.