I've been shooting wildlife for close to ten years now, with birds being my primary subject. I shoot canon, so there are a lot of lens to choose from. As with most things I don't think there is one best lens for every situation, it depends on the subject, the location, and the time of day, just to name a few of the many considerations. I generally shoot off of a tripod, with a Wimberley Head, if I am going to be at one primary location and it's less than a few mile hike to get there.
I find shooting off a tripod to be fairly easy, but you are limited vertically somewhat. I will usually use a long lens off the tripod and have a shorter lens mounted to a second camera. For reach limited situation the two main canon tripod lens are the 800MM and the 600MM. Both are IMO too big to hike with and hand hold. They are also too big to use in a car comfortably, although when I know my subject is going to be very far away I do it anyway (Snowy Owls). I have the 800MM and got it new as a Christmas present from my wife (Anne) in 2009 shortly after it came out. The 600MM lens appears to be much more popular now that V2 has come out and works with teleconverters very well. If you are going to use just one of the Canon big whites, the 600MM is probably the way to go. Personally, I prefer to use the 800 bare lens over a 600 with a 1.4x. I use teleconverters without hesitation, but I'd rather start off with the longest lens possible. In many situation a bare 800 is all I need. It works with both the 1.4x and 2.0x. With the 2.0x autofocus is limited to live view, but the autofocus on most lenses is so slow with a 2.0x I don't find this too big of a drawback. Either lens is a good chose, but to me the things that a 600 can do better than a 800, are generally done even better with a 500.
The main lens that I hike with and either shoot off a monopod or handhold is the Canon 500mm. I also use the 500 a lot when driving around looking for subjects to shoot out of the car or even sitting in the back yard. The F4.0 comes in handing in early morning light, which is my favorite time of day for this kind of shooting. For these uses the 600 would be better than the 800 in many respects, but this is where I believe the 500 shines as the best possible choice. I currently have version 1 of the 500 and upgrading to version 2 is probably next on my list of photography related purchases. The 500 I have is so sharp though that I haven't been in a huge hurry to upgrade. The reason to upgrade for me is the ability to hand hold more (lighter and better balanced) and the improved IS. I use this lens with both teleconverters version 3, and have no real issues other than slower autofocus with the 2.0.
The 200-400 with the built in extender is my next biggest lens. This lens is fantastic. The built in tele-converter makes this lens a 200-560, which is a great range. The 200-400/560 lens like most zooms is very versatile. It's usually my second lens when using the 800 off the tripod. I also use it instead of the 500 when I'm going to an area that I am unfamiliar with or don't need the extra reach (SW Florida for example). Also, if I am shooting mammals instead of birds, this is my go to lens. The nice thing about this lens is you can quickly get several types of shots with the same subject. A closeup zoomed in, and more of a environmental type of shot zoomed out. You have a lot of composition options that you can do without having to move, which of course in many cases you can't do anyway. This lens is similar in weight to the 500, but a little smaller. It's also a great lens to hike and travel with. When I travel by air, I generally take the 200-400/560 as my long lens due to the versatility. Finally this lens is great in wildlife parks, where the animals are a little farther away than in a zoo setting.
Update: I have also started using the 200-400 with an external 1.4 extender. This creates a nice 280 - 784 zoom range. Granted you lose a stop of light as always, so you are at F8 with both the external and internal extender in place, but works well on a nice sunny day.
135 F2, 200 F2, and 300 F2.8 - These three lens are good for shooting mammals and bigger subjects. I also use the 300 sometimes for birds in very low light if I can get fairly close to the subject. The 200 really shines in zoo type of settings where the enclosure has tightly framed bars, netting, or you can't get close to the enclosure with your camera. The F2.0 works magic in shooting through tight spaces. The 135 F2 works well in these situations as well. I generally don't use the 135 or the 200 for wildlife, but on occasion they are the best lens for the situation. The 300 is useable in more wildlife situations. Its hand holdable and since it's F2.8, you can get a 420 F4, or 600 F5.6. A lot of options, and a great chose if you don't need extreme reach. I also use the 300 as a second lens when shooting off a tripod in low light. The 300's reach can be increase by using a crop camera, and since it's 2.8 the ISO can be kept at a low level. I also have version 1 of this lens. I'll probably get around to upgrading this lens at some point, it's not a priority right now. The version 1 of the super telephoto lens were so good, image quality wise, that I've concentrated on better cameras and getting additional lenses, but getting the version 2 500mm is now top on my list.
70-200mm F2.8 IS V2 this is my second lens on most hikes and out of the car window shooting. I will use the 24-70 F2.8 V2 at times as well. Unlike the big primes I did upgrade both of these zooms fairly soon after the new version came out. I was never that happy with the version 1 lenses and I think there was a fairly big upgrade of the image quality on version 2. I will also use the 70-200 on a cropped body with teleconvertors as a light walk around lenses if I'm not in the mood to carry a big lens. The 70-200 is also a very good zoo lens. I find that this lens is wide enough to get some good landscape type of photos while I'm hiking around looking for wildlife.
Other lenses that I throw in the bag sometimes are the 14mm, great for taking pictures of large trees, as well as, wide open spaces. I also, use the 100mm macro at times for detailed wildflower or spider web shots.
Future purchases - As I mention I would like to upgrade my 500 to a version 2. Also, I will probably pick up the 100-400mm V2 as a light walk around wildlife lens at some point, but probably after the 500 upgrade. Down the road the 180 macro appeals to me, but it's so old that I suspect it'll be upgraded soon and I'd like to see what is improved before buying. The 400 V2 DO interest me as well, but it's not near as versatile as the 200-400/560 and it just may be a tad too short for a F4 wildlife prime. I've seen some great shots with it but in most cases people have indicated they wish they had a little more reach. I'm not sure I would have enough situations where I would use it over the 200-400/560 or the 500 to justify it.
Anyway, these are the lens I use most often for taking wildlife pictures, with some landscape shots thrown in on occasion. Thanks for reading!
Next time I'll review the camera bodies I use. With camera bodies the decision generally come down reach versus high ISO performance.
I did end up upgrading to the Canon 500MM F4, version 2. The biggest improvements for me over version 1 is the reduced and better centered weight, and the improved IS.
Also, I have picked up the 100-400mm V2 and the 11-24mm F4 zoom in 2017. The 100-400V2 is a fantastic lens as you have probably heard. It has cut into my use of the 70-200 F2.8 mainly and the 200-400/560 a little. Another benefit is that while I have been generally disappointed with the Canon 7D2, for some reason with the 100-400 on it, the camera seems to come alive. Also, the 160 - 640 effective zoom range in a light weight (relatively) package makes a great combination.
The 11-24 is my most recent purchase. I really like having a zoom for landscape work, but it's a huge lens compared to the 14mm F2.8. I could but the 14mm in a vest pocket, but the 11-24 is a little to big for that. I plan to use the 11-24 lens more in the coming months.