WHEN DO YOU HAVE TOO MANY SIDE QUESTS?

When they feel pointless and no fun, they shouldn't be there. That's really all there is to it : D haha.
I like when they give you more lore, or when they give you more character attributes and make you explore areas you wouldn't quite otherwise. They can be pretty fun as a distraction too.
I'm usually not too concerned about the timer (there are a few games where they buildup was so good it felt a little weird, like Okami, but I still loved it because it allowed you to stay in the world and roam a while before being locked in). It's really more about fun and utility.
As a rule of thumb naturally, fewer are better since it allows them to be done right.

If the player gets to the point where they have to stop and try to remember what their main goal is, you've got too many sidequests.

Micro-goals are fun and keep players engaged in what they're doing in the immediate sense. But players also need to know their concrete long-term goals, and always feel like they're working towards them, or they'll have no reason to come back to the game after putting it down. If they ever put the game down at the point where their next goal is "do some irrelevant shit that's out of the way," they'll probably never come back to actually do it. There's no draw to that. Most of FF15 feels like this, and a lot of Skyrim can easily feel like this if you try to do each quest as you pick it up. As a result, a lot of people never finish those games. They just get bored and stop playing.

LockeZ
If the player gets to the point where they have to stop and try to remember what their main goal is, you've got too many sidequests.

Or you could do what Elder Scrolls does and put in so many side quests that most people don't even realize there's a main story arc.

I'd say there's too many sidequests when they end up killing the pacing or urgency in the main plot, or if skipping the sidequests becomes a recommended tip for new players. (Like "get out of the Hinterlands" in DA:I, because that first area is frontloaded with piles of uncompelling fetch quests)

I enjoy sidequests that encompass a larger scope of the game, such as collecting Small Medals throughout a Dragon Quest game, or killing rare monsters throughout (like the Hunting system in Rogue Galaxy).

What I DON'T like is sidequests that bring the pacing of the game to a halt; ones that don't coincide or can be reasonably completed within your main objective, especially in more linear RPGs. I'd rather a sidequest tell me to kill 3 Whatchamacallits and collect two Stupid Rocks in the dungeon that I'm about to go in, or somewhere I will assuredly have a reason to visit later, and not somewhere 20 minutes out of the way. I dread being in the middle of a great story conflict or urgent part of the narrative and some bozo NPC tells me to go do something mundane a mile away. It feels like padding. And even a small handful of these can weigh down a story-driven game.

If the side-quests are optional, I don't see the problem with having an indefinite amount.

If you start pulling things like Xenoblade Chronicles X did where you either have to complete "side-quest x" to progress in the main story line, then that's not a side-quest. Or what they did with character-oriented side-quests where you were locked into them once you started, and there was a relatively rare glitch where you could be permanently stuck in them and unable to progress in the game as an event never activates to finish or progress in the side-quest.

I don't see a problem with the Skyrim or Fallout model of having thousands of quests, since they largely don't interfere with the game unless they add an item to your weight-based inventory that can't be removed until you finish the six-hour long side-quest.

Then there's Dragon's Dogma where most quests in the game can only be accepted and completed during small time frames within the main story line, leading many players to miss important items, or have characters disappear from the game forever due to not being rescued when the player may not have even known the quest to save them was available.

The only time I can accept side-quests is when they're a part of the main story—that they make sense.

For example, to use the example JosephSeraph put forth, Romancing SaGa: in that game, the player's character is just on an adventure and is a general do-gooder. There is usually a backstory to the character's position, but it's more the reason for the character being there, not a goal. Then, the main quest slowly unfolds out of all of the "side"-quests.

In other words, side-quests are bad when they compromise the goal of the game.

Side-quests are the random encounters of narrative.

The Elder Scrolls are a game about sidequests. One of the biggest problem with Skyrim it the fact that it tries to buck this trend with its main story, but does nothing gameplay wise to change the pace.

If you look at Morrowind, Caius Cosades straight up TELLS you "GO DO SIDEQUESTS FOR AWHILE" and you actually need to go and do sidequests before you can progress (although there are ways around this, like there are ways around everything Morrowind). In Oblivion you're told "go to X place and meet Y", but you're free to blunder about on your own. The main quest encourages you to close Oblivion gates, its biggest sidequests. It wants you out there, exploring. Skyrim, on the other hand, has story missions like "LET'S RUSH TO THIS POINT AND FIGHT A DRAGON OMG RIGHT NOW" and then you are free to fuck off and loot 9012 tombs. The story missions are almost all structured this way- time is of the essence, let's get to it right now!- which is totally opposing to the meat of the game. In my opinion, the faction related quests (which are almost as in depth as the main story is) are better structured for the reason people play Elder Scrolls. If you have sidequests, they need to compliment your game's style.

If your game is linear, then you sidequests should be, too. Like SgtMettool said, having quests as optional objectives to encourage exploration is perfect. Going into a big cave? Reward the player for finding 3 Fungus that are out of the way. Finding 3 Fungus is a shitty quest on its own, but if you're in the cave anyway, it becomes a little bit more meat on an existing bone.

If your game is open-world, every sidequest should have some ramification on the world, even if its tiny. The Elder Scroll sidequests have no real point other than to get a pittance of gold and some useless experience. But having sidequests that open up new merchants or NPCs, or alternate routes for the main quests... oh baby, now you're talking.

Your best bet for sidequests to make a thousand of them and then trim down, combine, and optimize them until you have a handful for each area. A few small, one or two medium, one big. Combine ideas into quest chains. Like Liberty said: you give someone some gold, and he heads to a nearby town. Maybe you help him out again, and you find him in some other town. Now he's on his feet, but he's got more needs. By the end, you've helped him, and earned a good reward. It feels like you've done something. Fetch quests are stupid, but not if they actually have an impact. "Fetch three pieces of iron ore and I'll give 11 moneys" is boring, but "fetch three pieces of iron ore and I'll sell you iron goods" is already better. While you're fetching three pieces of iron, maybe you found the last guy who went to fetch the iron. Maybe he's dead. Maybe it's a trap. Maybe necromancers have been hiding in the cave and townspeople have been sending people to die there. I don't know, use your own dang imagination.

The question "how many is too many" is always answered by "when it's not fun". So long as it's fun, the more the better. If you're just adding sidequests to say they're there (like every MMO) then you've gone too far. If you want a strong narrative and your sidequests are killing that, then stop. Of course, players are willing to forgive a slow story if the bits in between are super fun, so...

I think how the sidequests are handled is more important than their quantity.

Consider if they're passive progression and fall more under game balance. Like, say you're going to a volcano next. So you pick up sidequests to collect 5 volcanic rock, slay 3 hotdog enemies and copy down the text from a tablet found there. It promotes exploration of the new area that you're going to be going to anyway, and since players are more likely to do it you don't have to worry about the balance as much. If you finished the volcano and then side quests opened up to make you go back in, especially if the game doesn't have a mechanic for harvest points or anything else interesting, it can get super boring and new areas might be too difficult if the dev was expecting you to do those backtracking quests.

Also, while I think character quests should be avoided entirely, people seem to like them so I'll mention them. Consider if some side quests will advance character development or lore. For example, I remember in Shadow Hearts 2 I never even used the fortune teller character much and it wasn't until a long while later that I learned everything interesting to her character was in sidequests that I didn't do. So if you are going to use sidequests to expand on characters, make sure that's not the only place it is.

I like to think of sidequests as an additive feature. Sure, you've got the basic game lore and characterisation - enough to make your characters and world feel well-rounded if you're doing it right - but sometimes there's bits to their stories that you can't really put in the main quest of the game. That's where sidequests come in handy. They become an in-game DLC, the payment being the time you spend on them.