Playing umodded Skyrim I've encountered multiple large (quest ending) bugs and a huge amount of small (non quest ending) bugs. With the fanpatches there are still some bugs, but not nearly as many as there were before. Yeah Skyrim is a huge game but the other games I own that are of similar/comparable size didn't have anywhere near that amount of bugs (for me at least).

Name one. All the other games with the same world sizes and the same quest complexity are also by Bethesda :D

If I understand it correctly, the bug doesn't occur on the main quest - it occurs when a particular combination of quests appears.

Here are just a few bugs I can remember off the top of my head: being unable to progress in Laid To Rest, The gate guard in Riften refusing to talk (making it impossible for me to enter Riften in a normal way), the trap in the Ratway Vaults resetting and then being unable to be broken (unless you use a spell I think) again, the gate guard in Whiterun doing his dialogue sequence twice (not quest breaking, just annoying), Legend of Red Eagle quest resetting itself, occasionally cannot interact with quest important NPCs.

Not bugs, I know there are loads of bugs in TES if you happen to be unlucky. One game which is as big and as complex as Skyrim,

Now to elaborate a bit: I'm not actually excusing Bethesda for their bugs. I'm glad they are there since if they weren't, their games would be way smaller and I wouldn't want that, but bugs are always unexcusable. I'm just saying that they're not relying on modders to fix them - it's just extremely difficult to do so by themselves while retaining the scale of the game, and Bethesda then does what they can to release patches.

The problem began with this main quest: A Cornered Rat.
Esbern would refuse to talk and open the door.

Well that does suck :-P Still, I know of at least one person who got trough the storyline on the first playtrough after buying the game, so I suppose there's more conditions to replicate it than just that. And it doesn't change the claim that Bethesda 'makes games for players to mod' - for the simple reason that they also do console releases

No doubt about that. The same friend of mine managed to be a hell of a completionist on PS3 Oblivion. Till it decided that 500 hours are enough and would refuse to load dungeons anymore. Part of the reason why he decided to go with PC for Skyrim, because he didn't want to get burned again. (Especially with those problems that PS3 Skyrim was suffering from, at least initially.)

Had that same problem. Needed a couple of tries to create a sequence of console cheating and leaving the area and returning that the script would continue from that point :-/

At the moment I have several broken side quests I cannot complete. Some radiant quests (Kill the bandit leader, Get the book) because I cleared the location before (for another quest!). And Blood on Ice is totally broken, with the main protagonists standing around in Windhelm market and being invulnerable and not talking.
Also, it's sometimes raining dead dragons ;-)

Speaking of clearing areas before you are sent there on a quest, some named enemy NPCs respawn if you encountered/defeated them before a quest tells you to.

And sometimes, corpses of dragons just stay where they are, refusing to disappear. It's amusing watching a corpse of a dragon near a town's main gate and the people passing by, not even batting an eyelid.