There are some useful options out there, and I don't even know where to start, because I'm such a perfectionist...
UPDATE: the one to go for is listed at the bottom of the post, and it's STATCOUNTER. Read further if you want to know the details...
Following the advice of this post
Sitemeter looks pretty useful with a web interface for observing stats.
I liked the simplicity of Easy-Hit-Counters but never got around to testing it out because their policies.php page was a dud. Hmmm...
There are also these guys to consider (but I didn't look into them with much vigour):
I almost settled on BRAVENET because it offers a CSV download option, and has what seems to be a host of basic functions that I'd like. To register wasn't too complex (by today's standards) and it seems to allow me what I need. There is also a bunch of free tools for web-based stuff, but obviously we're only looking for a free counter right now. I didn't realise it was ad-supported, so that may not be ideal but I tried it out anyway. Alas, I couldn't get the thing to work quickly and easily with my modified template code, so I discarded it to the "almost-winner" category!
This is probably the best service to take, for simplicity of registration but depth of functionality. I was fond of BRAVENET and all its host of features until I discovered it wasn't very XHTML friendly. Statcounter lets you set some nice control, and the blog above recommends using this one (or at least, shows you how to set this one up).
What I especially like about statcounter is that you can keep multiple sites in different projects under one login.
Text / graphics? Pageload / Unique visitor? This site offers a lot of depth AND it has a great tutorial to set up the counter on a BLOGGER site (and many other blog sites!).