Assuming we are not in South Korea, parts of Scandinavia and urban/city mainland Europe and if it is just for internet then no leave it alone (even in those places speeds are not enough to make a real difference).
If you are dealing with internal networking then maybe, if it is just streaming and it works fine at present then leave it.
If you do a lot of file sharing (as in network file shares not p2p) for backup or transfer purposes or you have a decent streaming setup (more and more people are making servers/NAS boxes for their home networks and the hardware to use them the other end) then maybe.
If you are planning to run cables through your house then I would strongly consider "future proofing".
From
http://ezinearticles.com/?CAT5-vs-CAT5E-vs...6&id=322715 :
# Cat5 = If you plan on running at most 100 Mbps
# Cat5e = If you plan on running at 1000 Mbps (1 Gbps)
# Cat6 = If you plan on running at 1000 Mbps (1 Gbps) or more. Cat6 is better if you are in areas that have lots of interference like near power lines, lights, manufacturing equipment, or a long distance 1000 Mbps (Gigabit) run.
Remember wireless G (and given N is yet to be a firm standard) is only 54Mbps and most network hardware (especially consumer grade modems and routers) do not do gigabit all that well if at all.