Have to give an upvote to another civ that's fun to play as (which is why Egypt will be next) but I do wish the AI can learn to play the Mongols better. I would love to go against them as I play them.
I usually find the Mongols an entertaining opponent (although "rival" is a better term - in most games they end up as long-term allies), and they're often very strong (the game I just finished being an exception, but while they were no threat to me they did eliminate Askia. Twice), but what they aren't in the hands of the AI is a formidable warmonger. The AI struggles in any event with 'unconventional' UUs - just as it tries to defend workers with battering rams as though they're spearmen, and is hesitant to attack cities with them, it has difficulty with a ranged UU replacing a melee unit that can't take cities. Along with Egypt and Russia, they're one of the civs I most often come up against as a serious rival for victory (in one game they actually did win diplo victory before I reloaded - something I rarely do but did in that case because it was so close).
Songhai: As has been said before, while amphibious is nice, defensive embarkation is not as good in G&K; their UU is lackluster; their UB is good but nothing to write home about and doesn't complement a warmongering strategy.
I think people are looking at Songhai the wrong way, and it sounds as though people voting on them are either theorycrafting or not playing them correctly. It's first and foremost an economy-driven civ. The UB complements it by not costing maintenance (and a maintenance-free temple can complement warmongering through Holy Warriors) - and the money can be used to buy an army. It's a different approach to a domination civ than powerful units or German cheap unit spam; you make your money, then go out and buy an army. The UU isn't good, but it does the one thing that it needs to to complement the UA - gives you a high-strength medieval melee unit that can take cities without penalty, and taking cities = more money. It's a very tightly-designed civ, and that means that the UA, UU and UB don't look especially good in isolation because they are designed specifically to work together. The Conquistador is simply a superior unit to the Mandelaku in every way - however it doesn't provide Spain with triple gold when the cities get captured, or indeed mesh in any very obvious way with the Spanish Natural Wonder UA. With very early gold and going Honor to complement your barbarian-hunt, Songhai can get a very early lead in both gold and culture that can boost them ahead of the pack for much of the rest of the game - and because they're buying their army more quickly than other domiination civs, they can go on the offensive pretty early.
As a general point, I think people are to a large extent looking at all the civs here and asking "what bonuses does this civ add to the predetermined strategy I follow in every game?", which surely misses the point of playing different civs at all. There have been objections to Sweden on the basis that people don't make enough friendships, or only produce GPs they want to use for things other than CS influence. Objections to Songhai on the basis that you only typically run into a small number of camps if you play a typical game where you don't actively hunt them. Wasn't there someone who said they don't get enough Golden Ages to make Persia useful?
For me at least, the more interesting civs - and usually the ones that prove to be stronger than those that just give a passive bonus to what you're doing anyway - are the ones that benefit most from playing in a way unique to that civ. If I play Sweden, my entire game revolves around playing for CS favour and maximising Great Person production. I'll even build The Louvre to that end - a Wonder I would rarely build otherwise since it comes too late and either an extended Golden Age or two landmarks aren't relevant to a culture victory by that point, and it's of little use otherwise.
If I play Songhai, I hunt barbarians actively, I take Honor primarily for the opener in the early game and the closer for the rest of it, and will speed through that tree. I may even give cities I capture back to another civ so that I can capture them again later for another gold boost (I only need the capitals, after all).
etc. etc.