My opinion isn't much different, so I won't be wasting my time writing it all over again. Furthermore, it seems like everybody here has similar opinions, kappa.Now, for my personal input on the matter: Games with great replay value, hmm..
1.) Skyrim. Procedural quest and event generation take the cake, along with a nice story line and carefully crafted lore to top it off. Very delightful. And it actually has DLC worth getting. Back when Bethesda was still good..
2.) Insert Starbound or any other game that has procedural generations of quests and/or other things. You'll get an unique experience everytime, depending on how you look at it. Of course, the gameplay won't be much different. But hey, there's still roleplay for things like that..
Side note: No, I didn't forget Minecraft. It's just that I'm not too fond of it. Not because it's a bad game, but because of it's reputation. Many people have moved on, including me. I tried getting back into it, but I just couldn't. Kinda killed the replay value for me, tbh..
3.) Simulation/Sandbox games! (Think ArmA series. I doubt that anyone here plays it, though. I simply grew up with it. Otherwise, think about DayZ, a Survival Sandbox. Probably more popular. Either way, you get the point.)
Now, I get that all the things that I mentioned are sandbox games in their own right, but that's not the point. (Ah, well. One can hardly consider Skyrim a sandbox game. But if you try hard enough, you may just be able to..) However, I'm talking about dedicated sandbox games that got advertised as such. ArmA 3, for reference, can be almost everything. You just need the right scripts, mods and/or a nice community. DayZ on the other hand has randomly generated loot, interactions between players and a vast, beautiful map. There are times where you will survive, get lots of food and generally be happy and might even make new friends along the way, but there may also be times where somebody catches you, puts handcuffs on, steals your blood, puts a burlap sack on your head and releases you in a zombie infested town without any weapons, food or anything else to defend yourself or to survive. (Based on a true story. Not sure if I ever got my revenge, but I'm pretty sure I got someone who looked similar and had similar gear. I'm just going to pretend that I had my revenge because it's more satisfying that way. Anyway, you see? Unique experiences like that can make a multiplayer-sandbox feel so rewarding and exciting everytime you play it. Enough about that..
4.) Story-based games! The most popular example for this is probably Fire Emblem. Great games, really. Very unique and enticing. I played a lot of the games.
Playthrough count: Fire Emblem 6: 1.
Fire Emblem 7: Probably 3, maybe even 4.
Fire Emblem 8: 3.
Fire Emblem 9: 1.
Fire Emblem 13: I seriously don't know. Perhaps 5-7.
Now, needless to say, I've spent most of my time with Fire Emblem: Awakening. Not because it was good, also not because it had replay value, but simply because you had a lot of variety in the character cast. I had fun letting certain characters be classes that really didn't suit them. Archer-Chrom, for example, or War Cleric-Lissa without a Bolt Axe. (Seriously, without her magic stat, she's been absolute and utter trash. Her annoying, cringeworthy lolilike personality didn't make it any better.) To get to the point, Awakening did not have a great story, nor did it have much going for it, besides the OST and the endless possibilities that one had regarding gameplay. Especially with the StreetPass-Characters. Anyway, don't even get me started on Fates. While it may be better than Awakening in some regards, I still won't be buying it. I quite frankly do not like the direction in which the series is going. Too much fanservice for my taste. Still, there's people here who absolutely adore the game and I don't feel like judging or blaming 'em for liking it. Take it with a grain of salt and consider that it's just an opinion before starting to hate on me, alright? Thanks. Though, my opinion appears to be quite common. My favorite game in the series probably has to be Fire Emblem: Path of Radiance. Since it's replay value is pretty much non-existent, I won't go too much into detail. But it's safe to say that this game had made me feel emotions that I never felt before. Such as incredible anger against a fictional character. Said character has black, blessed armor. If you don't know who I'm talking about, then go play the game and see for yourself. Rest assured, I'll play the remaining Fire Emblem titles eventually. Not including Gaiden. I don't like Gaiden. xD
5.) Repetitive, boring games! Feel free to insert your own. I feel like my post has been long enough already. I'm thinking about stuff like Super Mario, though. I know that there's some variety, but most of the games are side scrollers. They may have their charme, but other than that, there's not much to it.
Anyway, this concludes my weird.. "list" thing. Keep in mind that it's just my humble opinion that is purely objective and by no means important. I actually didn't feel like answering, but now that I did, I come to realize that I really am too talkative.