The amount of misinformation in this thread is UNBELIEVABLE !
First, to answer the question, how far can you run an "Ethernet cable", the answer is,
for copper wire (i.e.Cat 5, Cat5E or Cat 6), 100 meters. In reality. I would not go past 90 meters.
There are many "flavors" of Ethernet. The "original" IEEE 802.3 (a.k.a. 10Base5)used a special coaxial cable about the size of your thumb (usually yellow or orange). Special "vampire taps" and clamps were used to tap off the cable. The clamp had a connector to an AUI cable to the port on your computer. (Yes, I am THAT old.) There were no hubs/routers/switches back then.
Next came "Thin Wire" (10Base2). It used standard RG58 (NOT RG59) coax and BNC connectors. An adapter box and AUI cable were still required.
The main advantage of these early version was that no hubs/routers were required.
Segment lengths are based the "Collision Sense" strategy of the protocol (the first 2 incarnations had multiple computers talking on the same wire at the same time). The 100 meter length had to do with the amount of "quiet time" you has to wait before trying to put your signal on the wire. Attenuation of the signal on the wire had nothing to do with the length (assuming you were using the proper cable).
Of course none of this really necessary tofay (except that the standards say so and for backward compatibility) because very few network use a multidrop cable as I just described. Most installations are using a star topology with a router/switch at the center.
Once the cost of routers got "reasonable" the alternatives for Ethernet opened up. 10BaseT, 100BaseT, 1000BaseT, fiber, etc.
BACK TO THE ORIGINAL PROBLEM !
The most reliable and fastest solution is waterproof/direct burial Cat5e cable.
225 ft for about $100 (you don't need Cat6 if you aren't going to run Gigabit). The simplest is wireless (802.11G or N). Wireless should not be a problem unless you are in a metal building or your antennas aren't very good (typical) or they are not located in an good location.
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