I agree with vivsin in part...the logo should be designed in a vector format and as I stated above that is how I design mine for the very reason he mentioned (vector formats are scalable) with that said though the question was not really what is the correct way to make a logo top to bottom but more so do most people make their own logos. Might be a good idea for a poll actually.
A logo's main job is to define a company via it's graphical elements and related "lettermarking" (text fonts) One quick glance at the logo regardless of it's size or format should scream the name of your brand to anyone who as seen your advertisements before. For this reason I have a hard time going along with his/her inferred statement that if it's not vector and only vector it's useless. Yes, you don't want logos to be too busy, keep them simple, but a little bling in the right proportion can be a good thing. And we all know raster is king when it comes to bling for the most part.
There are many companies that use both vector and raster versions of their logos especially when coming to web presentation vs. other advertising mediums. This makes the logo neither invalid nor useless and this approach has been used for successful private owned business as well as commercially traded ones.
Creating your logo as a vector drawing... yes it
will save you work, allow you or your client to be more adaptive, and always give you the same start point and quality reguardless of the size you need it to be. It's the smart thing to do for the safety and efficiency of you and your client.
but... if you are just making a logo for your small buisness and don't want to buy or learn vector design then all I can suggest is make that logo file huge

(both in dpi and dimensions) resizing down has a little better result then blowing an image up.
Regards,
LokiZ
BTW Vivsin, Sharp site and exceptional sample work
LokiZ