In Fate/stay night, all of the Servants’ alignments can be viewed on their respective status screens. The first part indicates the principles they consider important, and the second part indicates personality.
Below is a complete list of alignments featured in the game, for comparison purposes.

Saber Lawful Good
Lancer Lawful Neutral
Archer True Neutral
Rider Chaotic Good
Caster Neutral Evil
Berserker Chaotic Insane
Assassin Lawful Evil
Kojirou Neutral Evil
Gilgamesh Chaotic Good
Saber Alter Lawful Evil

While a difference in personality generally won’t be too much of a problem, a difference in principles will inevitably lead to friction.
Saber and Gil would be a good example of that.

Fate/side material: Fate Encyclopedia