For fans of major manga series that are being adapted into anime, it can be an exciting time. However, it is often more than likely going to be a frustrating experience overall. Most long running manga series that get adapted into anime before the original subject matter is concluded gets packed full of filler. These "filler" sections are new content that gets produced into anime to fill the time slot, opposed to the "canon" content that is the story of the manga. The primary reason filler exists is not to enhance the story, but because the anime can cover a larger span of subject matter. Episodes can cover several chapters of a manga so the anime eventually catches up. Thus the producers need something to fill those weekly episodes while the manga pulls further ahead.
For those that were fans of the original subject material, it is just painful to watch the filler. Occasionally they are interesting, but more often they are boring and introduce some plot holes that will likely never be filled. Mainly, it is just hard for fans to have to wait to watch the content they know and love week by endless week.
Bleach is one such anime that is riddled with filler. It is not quite Naruto filler bad and some of the filler arcs are actually kind of interesting. For those that didn't know what filler was until now and never read the manga, go ahead and watch the Bleach anime in its entirety. However, for those that want to watch only the canon Bleach storyline, here is a brief guide on how to do that.
Note: Some filler sections that have canon content exist, but most of it is only for a few minutes and not really worth sitting through what is almost a full filler affair. Regardless, the sections with canon content are marked. I may have missed some, let me know in the comments!
The beginning of what season starts during the section is marked as well. Some seasons are full filler, so those buying season boxsets (because we all, of course, are buying them and not getting them from anywhere else) will want to be aware before buying.
Soul Society Arc
Watch episodes 1 - 32 (Season One / Season Two)
Watch episodes 34 - 49 (Season Three)
Watch episodes 51 - 63
Skip 64 - 109 (Bount Filler Arc) (Season Four / Season Five)
Arrancar / Hueco Mundo Arc
Watch episodes 110 - 127 (Season Six)
Skip 128 - 137 (Season Seven)
Watch episodes 138 - 167 (Season Eight)
Skip 168 - 189 (Captain Shusuke Amagai Filler Arc) (Season Nine)
Watch episodes 190 - 203 (Season Ten)
Skip 204 and 205
Turn Back the Pendulum Arc
Watch episodes 206 - 212 (Season Eleven)
Skip 213 and 214 (Season Twelve)
Fake Karakura Town Arc
Watch episodes 215 - 226
Skip 227 - 266 (Zanpakuto Tales Filler Arc) (239 has exactly 3 minutes of canon content around 15-18 minutes in) (Season Thirteen)
Watch episodes 267 - 286 (Season Fourteen)
Watch episodes 288 -297
Skip 298 and 299 (299 is technically filler, but is based on the special manga chapter "Imaginary number 01. the unforgivens." that Tite Kubo released to promote the 4th Bleach movie)
Watch episodes 300 - 302
Skip 303 - 305
Watch episodes 306 - 310
Skip 311 - 341 (Season Fifteen)
Substitute Soul Reaper Disappearance Arc
Watch episodes 342 - 354 (342 only has canon content near the end) (Season Sixteen)
Watch 356 - 366 for the final stretch to finish up the anime!
....annnnd that's the end of the anime, for now at least. The anime is expected to continue once the manga nears its end or comes to a complete conclusion. The manga has entered its final arc, but no one is quite sure when it will come to an actual end. The author Tite Kubo seems to be drawing it out a bit too much, but it should make for some action packed anime. When the anime does return, they promised no fillers, but the trade off is that there is likely to be a long wait until then. So there's that at least.