It all depends on the sweep and how it's being administered.
I'd say the majority of sweep wins notify by email and of those "MOST" include a Congratulations in the subject line (but not all, so you do tend to have to read some messages more closely)... and a lot of the things that designate a normal email as "Spam" for normal email users are the same characteristics that winner emails contain, especially for one-entry or daily contests (the instant wins are more automated and timely, you're usually dealing with a real human for other wins).
So, email from an individual you don't know (instead of a generic newsletter mailer), sometimes with attachments will often be legit winners but will filter into Spam folders. Typically you don't have to fill out tax forms or an afidavit for wins unless they are over $600, but some sponsors use a less specific policy (if you wander through the forums you'll see discussions of the afidavits for She Knows and Big Prize that people get for much smaller wins). And some really well known companies work through much lesser known promotion agencies, so just because the email isn't coming from Marriott doesn't mean you didn't win from Marriott, etc. There's a bit of an art that comes with practice for spotting the winners among the swath of other mail that comes in on a regular basis and determining what is legit and what may be trying to scam you.
And while the majority will email, there are other sweep admins who will just automatically ship prizes with no notification, or will post your name on a
winners list on their site and never send an email, who will send a direct message through facebook, post on their facebook wall, send a direct message through twitter, and a few will place a phone call. From reading here a while, most will only call if it's a really big prize because they do a lot more verification and they want to ensure you are willing to accept the prize before they start putting you through the paces of all the paperwork.