I'll start by saying if you haven't seen X-Men Days of Future Past you should stop reading and go see it immediately then come back and read this. Huge SPOILERS AHEAD! This will focus on continuity in the X-Men series and what movies should be included.
When lining up the X-Men movie franchise there are plot holes that present themselves in almost every movie after the release of X-Men First Class. Although X1, 2 and 3 have certain continuity issues (no mention of the Raven/Charles relationship; no mention of the sentinel program which should have been a major issue at that point, etc) they still, for the most part, can be connected to The Wolverine, First Class and DOFP. The one film that has no connection to any other movie, other than the actors who play certain characters, is X-Men Origins: Wolverine and DOFP does a lot to further push it out of the loop.
Let's start with the timeline of events. In DOFP the past is set in 1973 while Origins is based in 1975. In 1973 (DOFP) Wolverine has an apartment in New York and is apparently working for a mob boss. In 1975 (Origins) Wolverine is fighting in the war and seems to have been there for awhile. Yes two years is long enough to possibly reconnect with his brother Sabertooth and join the war but it seems unlikely since he is nowhere to be found. With Raven being overseas helping mutants get back to the states you would think she would have come across Sabertooth. This is a hole but in a way it can be explained through off screen events that could have possibly happened (she did come across him but he did not want her help; Wolverine left immediately for the war) however there are more that are impossible to explain.
Next we'll look at the ages of certain characters. First off Stryker who appears in both DOFP and Origins as a high ranking officer in the military who works with outside sources in the fight against mutants. All that lines up nicely except that in the 2 years between the movies he ages about 20 years. Stryker in DOFP is a young man in his 20s/30s (1973) while in Origins he is a seasoned veteran in his 40s/50s (1975/1981). This was something I noticed right away. It's impossible to connect the two characters unless you give them some sort of father/son relationship. I believe however that they both are the same person which would make this the characters third portrayal in a X-Men movie. He was featured in X2 as a older man in his 50s/60s which lines up perfectly with the DOFP version. Other characters with age discrepancies are Charles and Emma. In First Class Emma Frost is depicted as a woman in her 20s/30s in 1963 and is "dead" in DOFP. At the end of Origins she is a teenager in 1981....I'll just let that sink in. Also at the end of Origins we see Charles as a man in his early 50s while in 1973 he is in his 30s. Other than being a blatant misuse of very important characters there is no way to connect these characters together with any of their counterparts in other X-Movies.
Last main point I'll touch on (although there are many more) is a scene from DOFP that involves Wolverine and Stryker. In 1973 future Logan recognizes young Stryker and proceeds to have visions of going thru the weapon x program. He hears the voice of and sees images of the older Stryker but it isn't the one from Origins. He pictures the one from X2 and he even sees the young Stryker age into the older version. If this alone doesn't tell you to erase Origins from your movie timeline I'm not sure what will.
With the timeline officially wiped clean after the events in Days of Future Past its safe to say that none of the previous events in X1, 2, 3 and the Wolverine ever happened. This will also save the franchise from these same sort of problems with future installments. Although I enjoyed most of the X-Men movies to date, that's probably the easiest way to completely get rid of the continuity issues. X-Men: Apocalypse is set for a 2016 release date, will be set in the 1980s and will feature young versions of Scott, Jean, Storm, Nightcrawler and Gambit (he was also in Origins (1981) as a man in his 20s but I'll leave that for another time). Let me know what you think.