OpenTTD is modelled after the original Transport Tycoon game by Chris Sawyer and enhances the game experience dramatically. Many features were inspired by TTDPatch while others are original.

Significant enhancements from the original game include:

bigger maps (up to 64 times in size)
stable multiplayer mode for up to 255 players in 15 companies, or as spectators
dedicated server mode and an in-game console for administration
IPv6 and IPv4 support for all communication of the client and server
in game downloading of AIs, NewGRFs, scenarios and heightmaps
new pathfinding algorithms that makes vehicles go where you want them to
autorail/-road build tool, improved terraforming
canals, shiplifts, aqueducts
larger, non-uniform stations and the ability to join them together
mammoth and multi-headed trains
different configurable models for acceleration of vehicles
clone, autoreplace and autoupdate vehicles
the possibility to build on slopes and coasts
advanced/conditional orders, share and copy orders
longer and higher bridges including several new designs, plus fully flexible tracks/roads under bridges
reworked airport system with many more airports/heliports (e.g. international and metropolitan)
presignals, semaphores, path based signalling
support for TTDPatch NewGRF features offering many options for graphics and behaviour configuration/modification
drive-through road stops for articulated road vehicles and trams
multiple trees on one tile
bribe the town authority
many configuration settings to tune the game to your liking
save games using zlib compression for smaller sizes, while not interrupting gameplay
significant internationalisation support. OpenTTD has already been translated into over 50 languages
dynamically created town names in 18 languages, plus NewGRF support for additional languages
freely distributable graphics, sounds and music
framework for custom (user) written AIs
zooming further out in the normal view and zooming out in the small map

Lots of effort has been put into making OpenTTD easy to use. These include:

convert rail tool (to electrified rail, monorail, and maglev)
drag&drop support for almost all tools (demolition, road/rail building/removing, stations, scenario editor, etc)
sorting of most lists based on various criteria (vehicle, station, town, industries, etc.)
mouse wheel support (scroll menus, zoom in/out)
autoscroll when the mouse is near the edge of the screen/window
sell whole train by dragging it to the dynamite trashcan
cost estimation with the 'shift' key
advanced options configuration window, change settings from within the game

Graphical/interface features:

screenshots can be in BMP, PNG or PCX format (select in game options menu)
more currencies (including Euro introduction in 2002)
extra viewports to view more parts of the game world at the same time
resolution and refresh rate selection for fullscreen mode
colourful newspaper after a certain date
colour coded vehicle profits
game speed increase (through fast forward button or by pressing the TAB key)
snappy and sticky windows that always stay on top and neatly align themselves to other windows
more hotkeys for even less mouse-clicking
support for 32 bit graphics
support for right-to-left languages
support for other (sized) fonts where the user interface scales based on the font and translation

Posting a full list would be futile as it would mean updating this page almost daily, and even then some things might be forgotten. Play with the game to experience all the features yourself, or take a look at the Wiki for a more thorough listing and explanation of the features and possibilities available.