Well, it depends on the definition you give of "ideal wire" and the exact context you are involved into.
Usually in lumped element circuit theory (CT), a connection between two terminals is considered a piece of ideal conductor of zero length.
An ideal conductor is a conductor with zero resistivity, hence that connection can be considered like a zero ohm resistor.
In basic lumped element CT we assume the EM fields vary very slowly, so slowly to be almost stationary (i.e. constant with time). "Almost" here means that we can neglect all the terms of Maxwell's equations that involve time variations.
This also implies that any element in the circuit has physical dimensions that are much less than the wavelength of any signal component in the circuit. Moreover, it also implies that the whole circuit is much smaller than that wavelength (because we neglect the propagation delay of the signals in the circuit due to the finiteness of speed of light). In other words, in basic CT we assume that signals travel in the circuits with no delay other than those introduced by the lumped elements.
That assumption, together with the fact that those connections have zero length (well, to say things more precisely, they have dimensions much smaller than the lumped elements they connect), also imply that there are no parasitic effect.
All this is a really drastic simplification.
When you begin to relax your definition of "ideal", e.g. you assume connections are made with a conductor having some finite dimensions and non zero resistivity, you get what other have already said in this thread: parasitics.
In particular, some residual series resistance (due to non-zero resistivity of the material. Conductors having length also give you some stray inductance, because of them forming loops in your circuit and being coupled magnetically. Their proximity makes them develop stray capacitance between different parts of the circuit.
Moreover, if you begin to take into account also the dielectric that separates the wires (e.g. FR4 circuit board substrate) this both affects stray capacitance and introduces some parallel (leakage) resistance.
Another problem with "ideal wires" having non-zero physical dimensions is that the resistance of the conductor varies with frequency (no, I'm not talking about the equivalent impedance or its real part, just the raw resistance of the wire) because of the skin effect and the proximity effect (ouch!).