A general rule of thumb is that if the original game has levels, and most or all of them are recognizable in the new game, but it is also clear that the developers re-created them, then it's an enhanced remake.
This group does not include "enhanced ports" where the game may appear to be enhanced due to being on a technically superior platform, and some features may or may not have been added, but the bulk of the game is simply ported and not re-created.
Edit Add Games History
Publisher : AGD Interactive, LLC
MobyScore : 4.03
Publisher : Microsoft Game Studios
MobyScore : 4.26
Publisher : Nintendo of America Inc.
MobyScore : 3.65
Publisher : Revolution Software Ltd.
MobyScore : 3.96
Publisher : Her Interactive, Inc.
MobyScore : 3.17
Publisher : Tecmo Koei America Corp.
MobyScore : 2.67
Publisher : Activision Publishing, Inc.
MobyScore : 3.00
Publisher : Devolver Digital
MobyScore : 3.57
Publisher : LucasArts
MobyScore : 3.52
Publisher : Gameloft S.A.
MobyScore : 3.92
Publisher : 1C-SoftClub
MobyScore : 3.73
Front cover for Halo: Combat Evolved Anniversary
Front cover for Archon Classic
Front cover for Earthworm Jim HD
Front cover for Tecmo Bowl Throwback
Screenshot from Halo: Combat Evolved Anniversary
Screenshot from Archon Classic
Screenshot from Robotz DX
Screenshot from Serious Sam HD: The First Encounter