Particularly keep in mind sequels you doubt might happen but you want to see. However it doesn't have to be just that so put whatever you want. If you really can't think of 10 games do 5 or 7.

1. Half Life 3- I honestly don't see it happening anymore which is bullshit since they can't end the series like that.

2. Fallout 4- I know this is well into development but I can't fucking wait.

3. Resistance 4- Resistance 3 is probably the most underrated FPS and maybe PS3 exclusive. Amazing campaign and I really want to see them go a bit more with the dark horror vibe since besides Metro there is nothing else.

4. Metal Gear Splid 5- Again this is bound to happen and again, I can't wait. 

5. Okami 2- I know there is a DS sequel but I want a new complete console sequel. 

6. Jak 4- Love this series. If Sly and Ratchet get to stick around, Jak has to be given at least one more game.

7. Heavenly Sword 2- I have not even played the first game (only the demo). I see a ton of potential with this though and with God of War winding down Santa Monica has the perfect IP to use as a sister for Kratos. They need to at least give it one more shot considering how easy it will be for them to make a sequel. 

8. Batman Arkham 3- I can bet this is happening and hopefully it will be a complete open world sequel with all kinds of characters to interact with.

9. Mass Effect 4- Bioware has really turned me off with their bullshit however I can't deny I love Mass Effect and I'm interested to see what the future holds.

10. Beyond Good & Evil 2- I haven't played the first yet (I will soon). Still it doesn't even matter it has been way too long since the first game came out and it's about fucking time that Ubisoft uses some of that spare change from Assassin's Creed to bring back a series with much potential and a devoted fanbase. Might be a lot higher once I can actually get into the first game. 

1. Conker's Bad Fur Day 2

2. Banjo Kazooie 3

3. Jet Force Gemini 2

4. Diddy Kong Racing 2 (Rare Racing)

5. Turok

6.  Legend of Dragoon 2

7. Pokemon Snap 2

8. ModNation Racers 2 (With different landscapes including lava and snow)

9. Persona 5

10. Jak IV

I cant think of anymore at the moment but ill come back t edit this for the other one

I'm going to stick with games that have not received a proper sequel yet, at least that I'm aware of (in no particular order):

1. Beyond Good and Evil (supposedly for next-gen systems, but no info yet)
2. Planescape: Torment (although a sequel is now receiving crowd funding)
3. Legend of Dragoon
4. Skies of Arcadia
5. Grim Fandango
6. Herzog Zwei
7. Vagrant Story
8. Psychonauts
9. Eternal Darkness: Sanity's Requiem
10. Jade Empire

1. Kingdom Hearts 3
2. Legend of Dragoon 2
3. Portal 3
4. God of War IV
5. Warcraft IV
6. Diddy Kong Racing 2
7. Super Smash Bros. 4
8. Pokemon Snap 2
9. Uncharted 4
10. Dark Cloud 3

These are what I could think of off the top of my head, at least. I'm sure I'm missing some that I would much rather see but oh well.

Star Wars: Battlefront III
Star Wars: Knights of the Old Republic III
Nothing else. Just those two, and I'll be happy.

@ OP - Wow, you haven't really lived long have you? Not a single game which hasn't seen a sequel within the last 5-10 years, and only two franchises which stopped 1 generation ago.

For me:

1. Super Mario RPG - Square Enix make amazing JRPG's and Super Mario RPG was one of their best games. A Uniquely Nintendo, and quality JRPG, a partnership like this again is probably something every Nintendo fan wants to see.

2. Chrono Trigger/Cross - Just the best JRPG ever, needs a good sequel

3. Golden Sun (GBA) - The DS game takes place like 20 years after the first 2. No, I want to see a sequel to the original trilogy (It ended at part 2!)

4. Metroid Fusion - I'd like to see a 1st person persepective on the main story Metroid games (1, 2, Super, Fusion). Metroid Prime was excellent, but I want to see a FPA Metroid game from a different time in the games history.

5. Mass Effect - Epic Trilogy, nuff said.

6. Lost Odyssey - The best JRPG of the 7th gen (IMO) by the creators of Final Fantasy with a story about immortals. The possibilities are endess, a sequel would be awesome!

7. Conker - CBFD was one of the best, funny as hell platformers around. Microsoft should really take advantage of this epic IP and make a proper sequel.

8. XenoGears - We saw XenoBlade, and are likely seeing a XenoBlade 2, but what about a sequel to the more traditional XenoGears? This was probably my favorite PS1 game.

9. Kirby's Dream Course/Tilt n'Tumble - Hey, an odd one, but these games are fun as hell.

10. Front Mission - Great franchise, tough SRPG.

1. Fallout 4
2. Kingdom Hearts 3
3. Legend of Dragoon 2
4. Star Wars Battlefront 3
5. Metroid Prime 4
6. Left 4 Dead 3
7. Mass Effect 4
8. Ratchet and Clank New Trilogy
9. Jak 4
10. Mario Galaxy 3

Battlefront 3
Metroid Prime 4
That's it for me.

1. Xenogears (Reboot) Eps I-VI
2, Kingdom Hearts 3
3. Chrono Trigger/Cross sequel
4. Star Ocean V
5. Lost Odyssey 2
6. Final Fantasy Tactics 2
7. Warcraft 4

What? Heavenly Sword and Beyond Good & Evil haven't seen any sequels. I don't see much potential for sequels to the PS1/N64 era and beyond.