From what I played:
RE3
RE4
RE5
RE Operation Racoon City
RE6 (garbage)

I managed to track down my old list. 

Here it is, with added summaries:

1. Resident Evil 4
Yes, Resident Evil 4 is responsible for transforming the series from survival-horror to third-person shooter, but it's also the most transcedent game in the series. The gameplay is rich and varied, the action set pieces and bosses are thrilling and terrifying, and the structure of the game a smart blend of action, exploration, and light role-playing elements.

2. Resident Evil Revelations
After the series strayed off course with Resident Evil 5 and 6, Revelations brought survival-horror back to Resident Evil. Set on a derelict cruise ship, Revelations deftly combines dynamic action with some truly harrowing segments. For the first time in a long time, players will feel helpless, alone, and underpowered.

3. Resident Evil 2
With stellar sound, graphics, and presentation, Resident Evil stands as one of the best of the series. The true star of the game, apart from excellent level and puzzle design, is the so-called "zapping system," which allows each character's storyline to overlap and inform the other.

4. Resident Evil Zero
Perhaps the most overlooked game in the series, Resident Evil Zero is an excellent addition to the Resident Evil canon. What makes it such a fun gaming experience is its "partner zapping" system, in which players can switch back and forth between two heroes, each with his or her own strengths and weaknesses. It adds a new layer to puzzle-solving and combat.

5. Resident Evil (2002)
One of the industry's best remakes, Resident Evil on GameCube made noticable improvements on the original game. Allegedly 70% different from the original, Resident Evil introduces new gameplay elements, rooms, mythology, cut-scenes, and voice acting, all to tremendous effect. The end result is one of the scariest games ever made.

6. Resident Evil: Code Veronica
While it doesn't compete with the best of the Resident Evil series, Code Veronica remains a great addition to the franchise, one with plenty of scary and surprising episodes. The first Resident Evil game to launch on a non-Sony system, Code Veronica provides all the features fans expect from the series: multiple playable characters, large-scale boss fights, and plenty of weapons and secrets.

7. Resident Evil 5
It might be a far cry from the origins of Resident Evil, but Resident Evil 5 is still a fun and thrilling shooter, one that becomes doubly better with a co-op partner. The sense of survival and isolation is gone, replaced with slam-bam action and co-op shooting mechanics.

8. Resident Evil 3 
With its branching paths and unstoppable villain, Nemesis represents a bold take on the franchise. Unfortunately the urban setting and focus on action detract somewhat from the overal experience. Nevertheless, Nemesis is an enjoyable game that's worth playing.

9. Resident Evil 6 
Featuring three campaigns, each of which follows a famous (or infamous) Resident Evil personality, Resident Evil 6 is a long, substantial game. But it's also a frustrating and sometimes hollow game, one so packed with interactive cut-scenes and quick-time events that it feels, at times, like a game on auto-pilot.

As far as Resident Evil HD goes, I will be passing. I already own the game on GCN.

1. Resident Evil 2
2. Resident Evil Remake (GCN)
3. Resident Evil Code Veronica
4. Resident Evil 1(PS1)
5. Resident Evil 4
6. Resident Evil 3
7. Resident Evil Gun Survivor

I will... I will buy Resident Evil remastered on Steam someday.

1. Resident Evil 3: Nemesis
2. Resident Evil 4
3. Resident Evil 2
4. Resident Evil (+ remake)
5. Resident Evil: Code Veronica
6. Resident Evil 5

Poor Resident Evil 3, I wish everyone else saw what I saw in that game!

5. RE5
4. RE6
3. RE4
2. RE: Code Veronica
1. RE: Outbreaks series.

I really, REALLY loved the outbreak series. I played RE1, 2 and 3 but I wasn't crazy about them due to the old graphics.

If you like REmake, i'm sure you will like 0. Its not a bad game, its just that the events felt just like an extension of the first game. It felt like DLC lets say. I no longer remember much of what happened. It also never felt like Rebbeca was someone who had gone through such an ordeal only to be a support character for Chris on the original (she should be alot stronger by then than she looked and acted like). Neither her nor Billy showed up in the series ever again, making the game events completely passable.

1. RE4
2. RE2
3. Code Veronica
4. REmake
5. Zero
6. RE3
7. RE5
8. Outbreak

Edit: @OP

I'm definitely buying REmake on Steam, at the right price of course.

I like the REmake but haven't played it in a couple of years. I understand where you are coming from. I haven't played 0 much yet but the game was featured in Umbrealla Chronicles and I did wonder why Rebecca never returned. I would say hopefully she comes back in 7 but I don't really want a RE7. Reboot or end it

1. Resident Evil
2. Resident Evil 2
3. Resident Evil 3
4. Resident Evil 4
5. Resident Evil: Code Veronica
6. Resident Evil 0
7. Resident Evil 5

The ones I truly played from beginning to end:

RE2 > RE5 > RE4 > RE3 > RE6 > RE:CV

I only watched LP of REmake and never got my hands on the original RE1.