In what year(s) does the Monogatari series take place? Looking from the perspective of the recent movie (which occurs at or near the chronological beginning of the series):


Koyomi has what appears to be a slide-phone with a keyboard, and Hanekawa puts her "phone number and email address" into it.
Koyomi goes to the bookstore for porn instead of just looking it up on the internet. (This show never seems to indicate any signs of the internet even existing?)
All the cars (which are mostly copy-pastes of the same CG model) seem to have a much older style to them.


Most of all, this frame (which appears right as Koyomi is about to bring up his phone) may indicate a year. But what does the "G9" stand for?
I don't recall an exact year, but there's evidence that the series takes place in the modern day, between 2007 and 2018.

The strongest piece of evidence comes from the novels. In Kabukimonogatari Chapter 7, after Koyomi travels back in time 11 years, he notes that the money is different and has Natsume Souseki on it. These would have been the series D bills issued from 1984 to 2007 and suspended April 2007. This puts the series no more than 11 years after 2007, or no later than 2018. The novel version of Otorimonogatari has Nadeko make a reference to K-On, also putting it after May 2007, when the K-On manga started.

Maroon notes in the comments that the dates line up better for 2006. The phasing out of the Souseki notes began in 2004, so 2006 is a plausible year as well. The novels began their run in August 2005, so it's possible that Nisio Isin looked to March 2006 as the starting point for the series.

Smartphones do exist in the world of Monogatari; in the preview on Episode 7 of Nisemonogatari, Kaiki complains that after Hitagi smashed his phone, he went to buy a new one and could only find smartphones, which he dislikes. Here's a hard-to-see picture of my television screen that shows it:



Flip phones are actually still pretty common in Japan; see this Answerman column. 

As a side note, the male protagonist hiding porn books in his room is a time-honored tradition of the genres that Monogatari draws on, harem and school action. Suruga also fills her room up with cheap BL books instead of going on the Internet and reading slash fiction. Monogatari is a mixture of real and hyper-real, so sometimes it just plays by the rules of fiction.