Storing a small number of images: blob or fs?
I once faced a similar question with a small DMS for pdf files. The scenario was different from yours: A maximum of may be 100 files with sizes up to 10 MB each - not what you expect for profile pictures. But the answer a friend gave me back then applies to your case as well:
Use each storage system for what it is designed to do.
Store data in a database. Store files in a file system.
This is not the ultimate answer(*), but its a good rule of thumb for starters.
I have never heard of the Windows FS being slow and sometimes unreliable, as Aaron Digulla states in his answer. If there are such problems, this certainly needs to be factored in. But for avatar pictures, it does not strike me as important.
(*) I know, I know, 42...
To answer parts of your question:
How do clients go with caching images from the DB vs from the filesystem?
For a database: Have a last_modified field in your database. Use the Last-Modified HTTP header so the client's browser can cache properly. Be sure to send the appropriate responses when the browser requests for an image "if newer" (can't recall what it's called; some HTTP request header).
For a filesystem: Do the same thing, but with the file's modified time.
If BLOBs stored in the DB are the way to go - is there anything I should know about where to store them? Since I imagine that a majority of my users won't be uploading a picture, should I create a user_pics table to (outer) join to the regular users table when needed?
I would put the BLOB and related metadata in its own table, with some kind of relation between it and your user table. Doing this will make it easier to optimize the table storage method for your data, makes things tidier, and leaves room for expandability (e.g. a general "files" table).
DB is optimized for latency, transactions, etc.
Image storage is optimized for read latency, storage cost, etc.
A blob store is ideal for storing millions of images. I work on SeaweedFS. It was based on Facebook's design for storing their user photos.