As
railiner stated and as others have indicated, there really is no easy way to determine current Amtrak routes, many changes of which have evolved since the advent of Amtrak.
Both nature ─ such as epically severe floods from stalled weather fronts and hurricanes (e.g. “Agnes”) and other phenomena ─ and mergers and consolidations since 1976 (Conrail), five years following the official start of Amtrak, have changed the passenger-run landscape dramatically. These factors alone have added multiple layers of complexity to the timeline of historical routes of Amtrak, analogous to layers of sediment in deep soil.
In part answer to the general question, it probably would be of more profound interest to know the timeline of such changes over an arbitrarily selected range of time ─ perhaps even as far back as 1964, when the Wabash and the Nickel Plate Road (NY, Chicago, and StL) were merged with the N&W which in turn merged with the Sou in 1982 to become NS. The reason I say this is that “modern-day” mergers began during the earlier portions of many readers’ lives ─ with a relatively short-span succession starting around 1957, with mergers of the NC&StL with the L&N (CSX predecessors), followed with the merger of the VGN with the N&W in 1959, and the Erie RR with the DL&W in 1960. Then came the merger of the SAL (Seaboard Air Line) with the Atlantic Coasts Line in 1967, as well as the ill-fated merger that became Penn Central in 1968, which laid to rest the single ownership of those involved former Class-Is. Many if not most) of us either have lived through or have at least heard of the many “fallen flag” lines dating that far back and which would be of interest to this topic.
And as
JameswhitcomeRiley pointed out, railroad ownership changes since mid-20th century have led to offloading of trackage to short lines, and in some cases abandonment of some segments ─ both minor and major. Add to that, the very recent merger of the KCS with the CP, in conjunction with proposed corridor and long-distance expansion, indeed will only confound this long-convoluted historical past of ownership.
All this only makes it (at least) somewhat challenging to recall the heritage of the current route of the “Capitol Limited”, for example, which does a “musical-chair” routine from WUS (WAS) to CUS. Without my going into too many details, It follows its original namesake B&O path between DC and the eastern outskirts of Pittsburgh. It uses a one-mile connection (via Schenley Tunnel) built for Amtrak in the 1980s to the NS (on the former PRR) line into Pittsburgh. It then follows the NS’ former PRR Ft Wayne Line (PFW&C) to Alliance, OH, where it diverges onto NS’ Cleveland Line (former PRR). In Cleveland at a point called "Silver Plate Junction", the line joins the NS’ former NYCentral New York - Chicago main. Finally, the route returns to the former PRR (at Calumet River Jct) for the last bit of run into CUS. Amtrak's current LSL follows a similarly "alphabetic" route.
So, some arbitrarily chosen time-period limit into the past would have to established for one to compose a reasonably comprehensive mapping of existing (and future) Amtrak routes, along what remains (and what could become resurrected). It would have to be updated periodically.