Even aircraft of the same designation changed drastically over the course of the war. A Gustav model Bf-109 had almost nothing in common with an Emil from only a few years prior. Early P-51s and late P-51s changed engines entirely. The list obviously goes on.
I was just curious, what ever happened to the older models when they were declared obsolete or combat ineffective?
There is not generally applicable answer to this because the answer may vary from nation to nation and even be different for different years of the war but in very general terms a few things happen to aircraft of older models when a significantly improved version is introduced:
Upgrades: If the frame is still largely unchanged, or at least can be relatively easily modified, the plane might simply be taken apart in the shop or factory and reassemble as a modernized version. Engines, guns, instruments and other parts can often be replaced so long as the airframe is roughly the same and mounts are not too different.
School planes: You gotta learn somehow. Oftentimes older, slower planes make for excellent training aircraft. Many a pilot in WW2 first left the ground in old biplanes.
Targets: I don't mean actually shoot the older plane to pieces but sometimes hauling a wooden target that someone else can shoot at is a viable use for an older plane. Target practice is valuable for both pilots and AA-crews. (Anecdote: I spoke to a few veteran pilots from Congo who were adamant that flying target practice for the AA-crews was far scarier than actual combat missions in Congo. They were constantly scared shitless that some raw AA-gunner would get itchy and mistake them for the actual target)
Secondary duties: Maybe the plane can no longer be used for its primary duties but who's to say there aren't other duties? Reconnaissance planes are oftentimes older model fighters or medium bombers. Bombers might be transfered to logistical wings etc.
Secondary theaters: An older model plane might not be able to go toe to toe with a modern enemy but perhaps there are other areas? Routine patrol missions in theaters were you are relatively sure you won't actually meet an enemy does not require the most modern fighters, you're just there as a precaution. CAS missions where there are no real enemy airforce to threaten you can still be very effective etc etc.
If you have specific questions about a certain nation I might be able to direct you to further reading or answer the question directly.