A route planner with no account or API key
Route by Zaweba plans routes and multi-drop rounds with no account, API key or paid map service, using free OpenStreetMap extracts on your own PC.

Yes, you can. Route by Zaweba needs no account, no API key and no paid map service. Its maps come from free OpenStreetMap extracts that you download once, and the routing, address search and map all run on your own PC afterwards. It is free software under its EULA.
That is unusual. Many route planning tools, and most of the code examples you find for building your own, rely on an online map service that wants you to sign up, create a key and accept usage limits. Route takes a different approach.
How it manages without one
An online planner sends each question to a server: where is this address, what is the best road between these points. The server needs to know who is asking, which is what accounts and keys are for.
Route keeps everything local. Map > Choose a region shows Geofabrik's list of OpenStreetMap extracts as a tree of continents, countries and counties, with sizes and estimates of preparation time and disk space. Pick one, and Route downloads and prepares it, building an address index, a routing graph and map tiles. After that one-off download, the map, routing and address search all run offline.
The routing engine is GraphHopper, bundled with its own Java runtime and reachable only from your PC. No network connection is used for routing.
What you get without signing up
Everything. Plan from A to B, choose fastest or shortest, avoid motorways, tolls or ferries in any mix, and drag the line to add via points. Build a round from search, right-clicks, a CSV file or a GPX file, give each stop a time at stop and a time window, and press Optimise order to put dozens of stops in the best sequence. Then export a PDF route sheet, GPX for a satnav, Google Maps links for a phone or the stops as CSV.
None of it counts requests or stops after a quota, because there is no quota to count.
Why that matters in practice
For a courier or a carer, the difference is reliability. A planner that depends on a service stops when the signal does, and in rural areas that can be often. Route plans in a car park with no bars as well as at a desk.
For a small business, there is no key to look after, nobody's personal account tied to the firm's planning, and no worry that a busy week will hit a limit. For anyone careful about privacy, the list of addresses you visit stays on your PC instead of passing through someone else's servers.
What it does not do
Being offline has trade-offs, and it is fair to be clear about them. Route has no live traffic, because live traffic needs a live connection. Maps are as fresh as the extract you downloaded; to pick up new roads, prepare the region again from a newer extract. UK postcodes come from OS Code-Point Open and cover Great Britain only, as Northern Ireland postcodes are not open data.
Setting it up the first time
Install Route, open Settings and choose where map regions should be kept, outside the app's own folder. Then use Map > Choose a region and pick an area. A county prepares in seconds to minutes; Great Britain is about 2 GB to download and needs roughly 8 GB of free memory to prepare, so start small if you only work locally. Once it is ready, type an address in the search box and start planning.
If you already have an OpenStreetMap extract as an .osm.pbf file, Use a map file I already have prepares it without downloading.
A route planner without an account is not a cut-down version of one with. Route by Zaweba is a full planner that simply does its work at home.