The range of possible scores in Ticket to Ride is 635. The minimum is -340, and the maximum is 295.
The minimum can only be achieved with two players. Your opponent keeps two goals, which must be Denver to El Paso and Kansas City to Houston. You must then draw every other goal in the game without playing any trains. You will get 0 for playing trains and -340 for goals. Additionally, your opponent needs to claim at least one route to prevent having a tie for longest continuous route.
The maximum points possible, 295, can be achieved by following the instructions given above.
However, achieving either a -340 or 295 is virtually impossible. To get -340, your opponent needs to draw Denver to El Paso and Kansas City to Houston and also throw away their third destination ticket. Since those two routes only require nine trains to be used, your opponent will likely draw a few more goals before you can take the entire deck.
Likewise, getting 295 is just about impossible. If you're playing against a real person, they will probably take at least one of the routes needed. Additionally, if your opponent takes one of the goals you need, it is impossible.
When playing against a stupid computer, the computer will also probably take one of your routes.
However, there is one way to make your chances of scoring 295 extremely high (without cheating). That is playing against a baby that doesn't do anything and forfeits all of their turns. This way, all you need is for him/her to not draw goals you need and for you to draw at least one goal you need per turn.