MySQL: multiple tables or one table with many columns?

Any time information is one-to-one (each user has one name and password), then it's probably better to have it one table, since it reduces the number of joins the database will need to do to retrieve results. I think some databases have a limit on the number of columns per table, but I wouldn't worry about it in normal cases, and you can always split it later if you need to.

If the data is one-to-many (each user has thousands of rows of usage info), then it should be split into separate tables to reduce duplicate data (duplicate data wastes storage space, cache space, and makes the database harder to maintain).

You might find the Wikipedia article on database normalization interesting, since it discusses the reasons for this in depth:

Database normalization is the process of organizing the fields and tables of a relational database to minimize redundancy and dependency. Normalization usually involves dividing large tables into smaller (and less redundant) tables and defining relationships between them. The objective is to isolate data so that additions, deletions, and modifications of a field can be made in just one table and then propagated through the rest of the database via the defined relationships.

Denormalization is also something to be aware of, because there are cases where repeating data is better (since it reduces the amount of work the database needs to do when reading data). I'd highly recommend making your data as normalized as possible to start out, and only denormalize if you're aware of performance problems in specific queries.

One big table is often a poor choice. Related tables are what relational database were designed to work with. If you index properly and know how to write performant queries, they are going to perform fine.

When tables get too many columns, then you can run into issues with the actual size of the page that the database is storing the information on. Either the record can end up being too large for the page, in which can you may end up not being able to create or update a specific record which makes users unhappy or you may (in SQL Server at least) be allowed some overflow for particular datatypes (with a set of rules you need to look up if you are doing this) but if many records will overflow the page size you can create tremedous performance problems. Now how MYSQL handles the pages and whether you have a problem when the potential page size gets too large is something you would have to look up in the documentation for that database.