RollerCoaster Tycoon and its expansions have a number of available patches that are highly recommended. RCT STATION has uploaded all of these patches online, for download here (broken link). This will update RollerCoaster Tycoon to v1.08.187, Corkscrew Follies/Added Attractions to v1.10.026, and Loopy Landscapes v1.20.013.
The 2003 Deluxe release, as well as all downloadable versions are already patched to the latest version.
There are two official roller coaster collection downloads from Chris Sawyer, both available via his website. While the "Cat" collection can be used in any version of the game, the "Phobia" collection can only be used in conjunction with games that have either the Corkscrew Follies/Added Attractions or Loopy Landscapes expansion packs.
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Setting the game to run in compatibility mode can help fix many issues with launching and playing the game. To do this, right-click the .exe, open Properties and set the game to run in Windows 98 / Windows ME, Windows XP SP2, or Windows XP SP3 compatibility mode from the Compatibility tab.
Some problems can be caused in Windows 7 and Windows Vista by having desktop composition enabled. To turn this off, check the 'Disable desktop composition' option from the Compatibility menu (right-click .exe > Properties > Compatibility).
Running RollerCoaster Tycoon with visual themes enabled can prevent the open/save dialog box from opening. To fix this, check the 'Disable visual themes' option from the Compatibility menu (right-click .exe > Properties > Compatibility).
Another save game issue can be caused by not running the game as an Administrator. To fix this, check the 'Run this program as an administrator' option from the Compatibility menu (right-click .exe > Properties > Compatibility).