Best vector format for logos

I would supply:

Original AI (in case they want to make changes)

EPS for older software such as vinyl cutters. 

PDF for more morder workflows; I would leave the color in same mode as it was created.

PNG (you can make various sizes quickly with the export for screens function),

If logo is a monochrome design, TIFF (a 1500 ppi, 1 bit/Bitmap mode, LZW-compressed; these can colored anything you want in page-layout programs, including white/paper)

SVG if they ask for it.

Anything else, they can make themselves or ask you for it.

Your clients need to tell you what creative applications they're using so you can tailor the art files to their work flow. That really should be established up front before any design work is done. The same goes for things like color modes.

The EPS format is outdated; one of the format's most serious limitations is no support for transparent fills.

The Adobe Illustrator AI format is supported by most rival vector graphics applications, but the level of support is very uneven. The AI files almost always must be saved down to an earlier "legacy" format, such as AI CS6. Current version Illustrator files will not open; or the rival graphics app will try to import PDF data, which can lead to unpredictable and wrong results. Newer Illustrator-based effects such as free-form gradient fills or gradients on line strokes won't be preserved when importing an AI file into Affinity Designer or CorelDRAW. Various "live" effects may not be preserved either. Graphics objects that don't have a bunch of live embellishments applied to them will import far more predictably into another target application. Generally speaking, logos and icons shouldn't have a bunch of live effects applied to them anyway.

SVG files are very hit and miss. If SVG files are coming from Canva they'll almost always stink. Downloading a "PDF for Print" file is the only thing I've seen that works at all from that web app.

PDF files can be very problematic. It all depends on what app is generating the PDF. Illustrator-generated PDFs (saved with Illustrator editing capability preserved) work very well. Just be sure to convert any live text objects to outlines so clients can avoid font substitution problems.

Other graphics applications that can save PDF files do not save PDF files that are edit-friendly. PDF files are not supposed to be edited. But plenty of us end up having to harvest graphics elements out of PDFs anyway due to inaction from clients. The Vector First Aid plugin can be an enormous time-saver when used to fix issues with artwork grabbed out of a PDF. Some problems may still remain though.

markeeeee,

You can look under Export here,
https://helpx.adobe.com/illustrator/user-guide.html

and especially under Export artwork, Collect assets and export in batches, andPackage files, and about PDF (also under Save).

With all this you can create a bundle of all (un)thinkable formats to cover all uses.

EMF can be used by Windows applications for vector artwork (within limits), and there is also WebP as an alternative to SVG.

PDF must be considered a must for print.

When starting, in order to get the best possible consistency of colour throughout, you can create the artwork in the narrower CMYK gamut for normal print purposes and then a corresponding RGB version for web/screen uses.

If you wish to work beyond the CMYK gamut limits, you can have a look at extended/expanded colour gamut,
https://duckduckgo.com/?t=ftsa&q=extended%2Fexpanded+gamut&atb=v320-1&ia=web

Edit: I had to leave for a while so there is a certain overlap with what Monika said.

You have to usually supply all of them.

So people can choose whatever is appropriate for the task.