Commonly used standard for telephone wires
Most POT (plain-old telephone) installations I have seen use wire pairs that are twisted very loosely (maybe one turn every 50...200&nbsp;mm) or not at all. There's one pair for each phone. Big cables with many pairs exist, and there's usually no shield.

Depending on the installation (try peeking behind one of your outlets!), you can get anything from two wires sitting loosely in a tube or being taped to wooden beams, ordinary and non-twisted cables to shielded twisted-pair wires lines.

A phone line needs two wires (unused wires may be preset in your installation); a 10/100 Mbit/s network line needs two pairs of wires (= 4 wires).

There is no short answer what bandwidth you can get over an unknown cable, but here's a bit of background information:

A network interface for a CAT5 installation has a defined impedance for the transmitting or receiving differential (two-wire) interface. The goal is to get as much energy as possible from the transmitter of one device (e.g. your DSL modem's PPPoE interface) to the receiver (your notebook's network card). Note that both interfaces contain a receiver and a transmitter, so there's also a differential (two-wire) line from the notebook to the modem, all behind the same modular 8-pin socket (often called RJ-45). This works best if the cable between the two interfaces has the same impedance as the transmitter and receiver. CAT5 is designed just this way: The wire insulation, the distance between the two wires of one pair, the way the two wires are twisted into one pair, the pinout of the connectors etc. are produced very carefully. A phone line, on the other hand, has very loose requirements, so you can have a line where the two wires are close to each other for a while, then form an open loop between them somewhere else, and the wiring behind your sockets may be a pure mess. Varying impedance, crosstalk and bad connections are just some of the bad things that will happen to your signal.

Long story short: If you need a cable for a network interface, it is a very good idea to actually use a CAT-(5, 5e or 6) type of cable. If such a cable is not available, at least try to run the differential signals over those wire pairs that look most like they could act as differential lines - and good luck!