If using hubs there is a limit imposed by the need for a collision to be detected everywhere, iirc it's officially two hubs for fast ethernet (though in practice you may get away with more due to shorter than required delays in the hubs) but hardly anyone uses hubs anymore so this is largely irrelevent in modern network design. Switches either seperate collision domains or eliminate them entirely so this isn't a problem on a switch based network. Eventually the delays would build up to the point where higher level protocols started to time out but the network would have to get huge for that to happen with most protocols.
Practically there are several other troublesome factors. One is that switches rely on storing the mac addresses of every machine on the lan to decide where to send packets. If there are too many machines for the switches to store the switches will "fail open" and end up broadcasting traffic they don't know where to send to the whole network. Furthermore being a tree network a lot of traffic will tend to cluster on the center of the tree (the impact of this can be reduced by making those parts of the network higher speed or by using techniques like port trunking).