How many completed routes is typical in Ticket To Ride (for each number of players)?
In my experience, the answer to your question actually varies less based on the number of players (except for at the very top end) than on what strategy you prefer to pursue. This is because the biggest limiting factor for the most part isn't route competition as much as it is simply running out of trains (or time, if someone else goes through their trains more quickly) to build more routes with, and those factors don't change as much with the number of players.  So how does strategy affect the number of routes you complete?  Well, the core USA version of Ticket To Ride supports a few different strategies, including most notably:


A 'transcontinental' long-route strategy, featuring routes like LA to Boston or Seattle to NY (tiny note: I haven't vetted any of these routes specifically; my copy of the game is at home and I'm not.)
A 'hub and spoke' type strategy featuring many roughly-parallel shorter routes, typically around the eastern seaboard and along the Mississippi River corridor; this might include routes like NY-Dallas, Pittsburgh-Houston, Duluth-Houston, etc.


For the transcontinental strategy, it's not unusual to have just two or three routes successfully filled, and to make a large proportion of points on the routes themselves, especially since the preponderance of five- and six-train segments run primarily east/west so they're relatively straightforward to pick up while completing one's routes.  Contrariwise, a successful shorter-route strategy will need many routes to work, often completing as many as 6-8 or sometimes even more.

One thing to note is that a number of players consider the base TTR USA set to be unbalanced in favor of the long-route strategy, for various reasons - a player who starts with the right routes to pursue that strategy is more likely to be successful than a player whose starting routes force them to play the 'short game'.  If you have the opportunity you might consider picking up the USA 1910 expansion for the game, which does a fine job IMHO of correcting many of the strategic flaws with the original game.