How do you handle seemingly random Steam friend requests?

Send them a message asking who they are.

I accept them and ask them why they added me, if they beg/try a scam i delete them, it's the best way atm (sometimes i troll the scammers but only if i got some time)

I usually accept all friend request I recieve and send them a message asking why they added me. If the just added me to add me, I normally delete them right away. If I got added by a scammer I hold them on for as long as I can and then delete them, and so on.

I usually accept any requests, but before that i check their profile in order to have an idea about their interests or taste in games. You can always delete them from your list if they are rude to you.

Enhanced Steam, or steamgifts.com/user/id/insert_ID64_here (would be http://www.steamgifts.com/user/id/76561198048004902 for me for example).

Also, what does being a woman on the internet have to do with it? As no-one can actually see that (I mean, people also ask me whether I am a girl or a boy).

I ignore them if they don't leave a comment, actually. But maybe I should add them and see what they want.
[EDIT] You can do what I do, say that you won't accept random friend requests unless they comment on your profile saying why they're adding you.

I try to figure out why they would add me, and if I can't think of anything, I block them...

But random friends are best friends!
(I'm adding you right now, OP)

Like every other person has said, add them and ask them what they want?

They aren't going to jump through the screen and attack you nor are they going to h4xx0rz your PC.

I handle them by creating a topic on a gaming forum that will inevitably end up attracting even more seemingly random requests... oh wait

What does a friend request mean. I don't know

Accept them, give them 5 minutes to state their business => Remove them if it's bull (it usually is :p).

Oh and dont click on links :p

I've had about 5 people add me randomly in the past couple weeks. I accept and just ask why they added me. Simple.

If I have a trade thread on Steamtrades, TF2 outpost...I usually accept the invites and ask them if they add me for trade. If not, I ignore them all.

Maybe they're just a bunch of horn dogs?

if i have no idea who it is then i just ignore it if they want something from me they can leave a comment ^^

Some of the steps I take: Check if the person's posted on my SteamTrades threads. Check SteamRep. Check if the account is new and how many games it has. Check SteamGifts to see if the user is a winner or creator. Check friends/groups in common. Accept anything that looks legitimate and decline requests from suspicious Steam accounts (new, few games, fake profile rep, friend with known scammers, trade banned, etc).

i'm antisocial so i dont get many, usually i go straight to SG and see what i've won lol. otherwise, ignore.