List below contains mosty/only unreplaceable tools with preference to core JOSM tools. They are grouped per function rather than per plug-in or Main menu.

Search among all JOSM tools and menu items - Ctrl+Spacebar

Basic shape of objects

• Select, move and rotate tools - you only need subset of tools from this list
• Draw a rectangular stub - optionally aligned along by other objects
• FastDraw - useful with natural objects;
• Extrude, Angle snapping, ​Spline or Bezier ''from commandline plugin'' - mostly for man made objects
• both Draw nodes mode and Improve Way Accuracy mode - have their followers and use cases
• Paste previously copied objects - not only tags but also their geometries

Selection

Selection (or list of currently selected objects) is precisely described in Help/Dialog/SelectionList#Selection (because it is visible from this dialogue), it can be modified with following tools (incomplete list):

• Select objects - contains many modifiers, including lasso mode
• Search - a very powerful tool and a query language with over 28 keywords and flexible operators to combine them in flexible manner. Not to mention regex and mapcss filters.
• (Shift+F3) - search objects by preset
• Help/Plugin/UtilsPlugin2 - multiple selection focused tools from UtilsPlugin2
• Select non branching way sequences - useful when editing highways, railways, rivers, power networks and networks in general
• Select all is more useful after you download precise list of objects

Tags

Tags of currently selected objects displayed in Tags/Memberships Dialog.

• Copy - copy selected objects to the buffer
• PasteTags - paste previously copied tags
• Tabular editor (Ctrl+T) (from UtilsPlugin2)
• (Shift+R) (from UtilsPlugin2) copy tags from previous selection
• Standard Add tag (Alt+A) dialogue provides 5 shortcuts to 5 last used tags without closing this dialogue

Topology tools and changes

• Merge two or more points
• UnGlue explode single point into multiple
• Join point into a way segment
• DisconnectNodeWay - opposite of above, disconnect a node from a way segment
• AddIntersections (Shift+I) (from UtilsPlugin2) - will create nodes at places where current selections intersects (or self intersects)
• Split geometry by selected line (Alt+X) (from UtilsPlugin2)
• Split way - split way by a node
• Combine Way - combine several selected ways in one
• Join overlapping areas
• ContourMerge mode can used to glue complex parts that would require too many Merges otherwise; it could also used to partially or completely replace geometry of one object with partial or a complete geometry of other object

Geometry tools

Precision in angles

• Anglesnapping will ease drawing way segments in 30°, 45°, 60° and 90° degrees
• Extrude tool will ease drawing of strictly perpendicular segments

Alignment

• Align in line will align selected nodes into a line
• Distribute as above, but also place them at equal distances
• "Copy" objects at precise anchor points from ​commandline
• "Move" objects at custom vector from ​commandline
• Align selected nodes in circle

Parallel

• Parallel, draw lines and curves parallel to each other, draw nested infrastructure quickly
• Extrude mode used on segments - will move them in parallel, preserving angles when it is needed

Rotation

• Rotate objects at user-defined angle (but exact angle is unknown)
• ShapeTools plugin:
  • Rotate object at predefined angle
  • Rotate objects (match building with road)
  • Rotate objects (match building with road, don't rotate more than epsilon)

Viewport control

• Explained at MapView, "View" menu and Zoom tool
• Minimap window
• JumpToPosition