During the build up to the release of 5th edition Dungeons and Dragons, Mike Mearls and the rest of the D&D team often claimed that one of the guiding principles for the 5th edition team was to make the game backward compatible. Put another way, players who loved prior editions of D&D should be able to still "play that way" with the new edition.
Now that I've been playing 5th edition for about a year, I can say with some confidence that I think this is true with regards to the 1st through 3rd editions of the game. Old school (Moldvay/Cook, BECMI, and 2nd Edition) modules are extremely easy to run under the new system with minimal prep on the part of the Dungeon Master. Modules from 3rd edition are similarly easy to convert as well, though the play will "feel" different. This is because high level 3rd edition characters, of the 3.x and Pathfinder variety, are EPIC in their capabilities where 5th edition characters are more modest. It might seem strange to say that high level 5th edition characters are "modestly" powerful, but in comparison to 3.x it's true. I haven't attempted to convert any 4th edition modules, but I think that should be easy as well especially if one uses the "post-Essentials" adventures.
As similar in style to older editions as 5th edition is, it has a nice mathematical core that echoes 4th edition but is toned down and has greater variation. In fact, it manages to add the variation of 1st and 2nd edition while maintaining some of the rigid predictability of 3rd and 4th edition. That's quite a feat. I'll focus a future post on some of the elegance of the mechanics of 5th edition for a later post, but it should be stated that the new edition makes "stat inflation" and "magic item proliferation" less important than any edition since 2nd. The amazing thing is that it does so while lacking the Dungeon Crawl Classics-esque funnel effect at low levels.
There are a few keys to adapting older edition adventures to the new system.
1) Stick to the more narrative modules.There are reasons for each of these recommendations.
2) Have your Monster Manual handy.
3) NPC are more work than Monsters, but often make the best opponents.
Narrative modules scale better with 5th edition's experience system. If your players are willing to remain at low levels for extended dungeon crawls, and there is nothing wrong with that, you can run the earlier modules. You will just have to guesstimate when to give advancements. A module like The Keep on the Borderlands scales fine with regard to the encounter difficulty, but players advance in level much faster than old editions and the players might end up with a cake walk if you use the current xp guidelines.
Most old adventures, and the Paizo adventures in Dungeon, use very simple stat blocks for monsters. In fact, the stat block is often [Skeletons HP: 8, 6, 9, 3; see MM pg. XX]. You can either make copies of the information before hand, which is what I typically do instead of opening the book, or you can have the book handy. Either works just as easily and requires no conversion. When there is no 1:1 monster, just substitute one you like or use stats for one you like while keeping the monster description from the module.
NPCs make the best villains. In 1st and 2nd edition, making NPCs was pretty quick. You decided on a level, rolled HP, picked spells and magic items, and DONE! This process got more complicated with 3rd edition because of all the feats, prestige classes, and item proliferation required to keep the NPCs competitive with the PCs. Not to mention spending all those skill points. Pathfinder, while being merciful on the skill point side, has a lot of options for DMs to resolve. Options are fun for players who get to use their characters for months/years, but for a one to three shot NPC the work isn't often worth the reward for DMs. Making Wizards, Demons, or Dragons for high level PCs could be hours of prep in 3rd edition. There are fewer decisions in 5th, but there are still some meaningful ones, but it's a more enjoyable DM experience for the working Dungeon Master. I put it that way because making characters can be a wonderful time, but when you are time constrained due to work, school, and family a faster process is preferred and 5th edition is faster than 3.x.
Having talked about the relative ease with which the modules can be adapted, and providing 3 guidelines with regard to adaptation, it's time to talk about why you should consider using older modules.
1) There are several available on DriveThruRPG.The rest of this series will be a series of recommendations of modules to use and include discussions of how these modules play in action. The modern player is often different in style to earlier gamers and no module plays "as written." I'll discuss some curveballs that I've seen during my sessions and how they made for even more enjoyable experiences.
2) They are inexpensive and average $5.
3) There are some genuine classics.