As always with a broad question like this, it depends. Some game systems have collaborative character creation as part of the process (e.g. Spirit of the Century). Organized Play (D&D and Pathfinder) requires you to bring a preexisting character. Some groups care more about tactical balance and want some character creation collaboration so they have someone in each "role." Others care more about plot and want hooks that tie the characters together built into their backplot. All are part of a continuum of valid approaches which get you different things - the things you get from the approaches are reasonably obvious.
You can just show up to the table with a premade character no one has had input into except, usually, for a definition of system/setting (A GURPS character and a FATE character walked into a bar...). This means you can get started immediately and have no constraints on your character choice. For those games that require "a tactically optimized team" or "everyone in one big mob all the time, working together with no dissent" this is obviously a weak approach. It's more suitable for a simulationist game.
Also, this is the approach used for Organized Play games where there is no "one GM" or even "one group". Therefore premade characters via a reproducible point buy system with no backplot anyone cares about are required.
Premake with Guidance
Often premade characters are made with guidance. The GM will a priori provide tighter rules or story guidance to the characters, who still make their characters offline. For example, we recently started the Jade Regent Pathfinder AP, and the GM sent what specific books were appropriate for us to use, other limitations and guidance (no evil characters, will have Asian flavor) and the Jade Regent Player's Guide dictates that we have to have preexisting relationships with four prominent NPCs that will play a large part in the opening of the plot. Sometimes the group works together offline for basic coordination - like "I'm going to be a TWF ranger, only pick this if you want to be competing with me in that role" or "Let's be a band of traveling entertainers as a starting group conceit." This constrains choice somewhat while still maintaining a fast start and giving a light level of organic guidance as to party roles and plot suitability.
A slightly side note here is games that have rolled stats where the GM watches you roll them ahead of time for anti-cheating purposes and then you build the character on your own time. The vast majority of games don't do this any more however.
Make at Table
In a super story or tactically optimized game, or in a game where characters are designed to be shed like the dust off your sandals, you can make them during the first session. It's good for preventing cheating, but will take a whole game session for most systems - even with simpler systems, some players really like to build a couple different characters, or build them out a couple different ways, or build them up to a certain level, before they are satisfied. Many may not want to do that, so it can create boredom. It also gives the GM and other players a lot more opportunity to fiddle with the player and their character, which might "fit them in better" but also constrains their freedom a lot more. It's also a lot harder to have any character secrecy; once you get to this level of character creation then mostly, everyone knows everything about everything else, which tends to hinder immersive roleplay and stories where there's not full disclosure. Also, some Design at Start people put more time into background than is usually contained in one game session, and this approach can make them feel rushed. It's also where you start to get conflict over different conceptions of gaming as people give provoked or unprovoked input into others' character builds, critiquing their mechanical choices, realism of backplot, etc. Maybe it's "healthy" to address those in the group and maybe it just leads to argument and hurt feelings.
Then there's games where character creation is in depth but more deterministic - like from a Lifepath sort of thing like Traveller; these can need more of the GM oversight throughout the process and can also be fairly entertaining for onlookers, so those are popular to do at the table.
In the previous approach, people may "talk" about each other's characters and say "you should be the cleric! And you shouldn't be Chaotic Neutral! And why are you putting an 11 into Charisma, you should just dump stat it!" Which is certainly a high level of meddling, but some games really do collaborative character creation where there's a formal system for it (GUMSHOE gives you a different number of ability points based on how many PCs there are and you're encouraged to make real sure all skills are covered together; in SotC and some other FATE variants you are supposed to weave other PCs formally into your backplot in a mini-lifepath sort of deal).). This tends to create a group of PCs with no mechanical gaps and with novelist-level backplots and hooks that "should" ensure that everyone gets off to a novel-style story. It takes a lot of time, sure, but it's ideally interactive so somewhat fun - but it also constrains the choice of the player a lot, risking them not caring so much (especially toxic for a story driven game).
Other Weird Options
In some games, the GM just provides characters - this is common for one shots but isn't unheard of for campaigns. This is for when the need for game mechanic auditing or for characters to have just the right background etc. are considered as being more important than the players' investment in the character - IMO always a dangerous play, as it signals moving from RPG into other more appropriate art forms.
Higher Level Characters
The history of D&D is rife with people asking about people who showed up with "their preexisting 15th level supercharacter" to a session and expected to play it. In 20 years I've never seen that or been part of a group that would countenance it for even a moment. Except for the Organized Play campaigns (since characters are strictly rules-bound), there's a general understanding that a character is in one campaign/setting and does not "port over" to another unless there's something quite specific and unusual going on. All my points above about bringing a character to the table assume campaign start chargen and not bringing a pre-played character.
I've games with a lot of people for more than 20 years so I've done each. I tend to prefer making separate with light pre-guidance, as I tend to prefer simulation and character immersion and that's the best approach for that gaming style. We do still do the others in special cases - "short couple session campaign of Blowback," or one shots, or games where the game prescribes an approach - but if it's something neutral then the GM provides loose parameters and the players toss stuff out by email to each other if they are the kind that likes to do that.
Because in the end people like a lot of different things about gaming. Things that are not going to be reconciled in a chargen session. We have one guy who kinda gets bored of characters and doesn't mind them dying to get a new one after a while. Other players don't do that. Some like to be secretive and have a big background that is a surprise in play, others don't care. The more chargen is shared, the more you are forcing a single approach, which is fine if you have a group of people that are really all aligned on their goals. Sure, too little of that and you can have misalignment in play - but that's a much more mitigatable syndrome. Like in modern society, people can believe all kinds of things as long as they act a certain way in public - it allows for a safety valve for diversity while allowing enough uniformity to make things work.