Rather alarmingly, I've noticed that quite a few people do not quarantine new cats that they've picked up. Someone just wrote in to ask if it was okay that she had put a new cat she had picked up with her own cat - she mentioned the new cat had some sort of bugs crawling on it.
Even if the cat looks okay (no ticks, mites, fleas, sneezing, runny eyes, etc) - new cats should NEVER be put with the existing cats when they are first taken in. They should always be quarantined and should be checked up by a vet. A lot of diseases are not immediately visible and may develop as time goes on. Check with your vet when it is okay to mix your own cats with the new arrivals.