I believe the + and - signs your first and second circuits are trying to convey different things.
In the first circuit it looks like the +ve and -ve terminals are the +ve and -ve terminals of a battery or similar voltage source. I say this because both the 30V battery and the 25 Ohm resistor are between the +ve and -ve symbols. It appear they are trying to say that the 25 ohm resistor is an internal resistance.
In the second both circuits the +ve and -ve symbols near resistors are to define the direction of the corresponding voltage drop across the resistor (eg what BvU said).
The basic procedure to follow when solving circuits like this is to first mark up the circuit with either +ve and -ve symbols like this or use arrows to indicate which end of any voltage you define to be +ve. It doesn't matter if you are wrong. The important thing is to be consistent when you convert your definitions into circuit equations (eg KCL, KVL).
So for example take a look at the 6R resistor on the right. For whatever reason the person that labelled the circuit choose to define V3 such that the bottom end is +ve. Now if you solve the circuit equations and find V3 turns out to be a positive number then the bottom end of the 6R resistor will indeed be +ve with respect to the top end. However if V3 turns out to be a negative number that means the top end of the 6R resistor will be +ve with respect to the bottom end. Neither is "wrong" although one appears slightly odd.
I suggest you work out V3 as an exercise.