I'd like to offer my own answer, which is probably a combination of what the others have written. In my opinion the blend is important.
1) Moving locations
It's unfortunate that you are so far away from your team. Moving your work space, as some have suggested, is typically not within your power. Where you sit is often very political in a company. You can try asking your team-leader to relocate you, but he would probably do that if he could. You're going to need to get around that.
2) Breaching the gap
Randomly walking over, as you've pointed out, is probably a bad idea. However, what about during lunch? Does everyone eat at their desks? Do they ever go out together, or alone?
I would start sending e-mails about an hour or so before lunch. There are several ways you could approach this:
Hey guys, I'm eating my lunch in the break-room, I'd welcome any company, since we rarely get to speak!
And keep eating your lunch in the staff room, which makes you approachable to them. Eventually they will reciprocate/join you.
Hey guys, I'm going out to grab a sandwich/pizza/chinese. Anyone else wanna join me? Other suggestions are welcomed.
This opens the door to them similarly inviting you when THEY go out. Offer to drive to sweeten the deal, if applicable.
Hi everyone, since we rarely get to talk, I was thinking that we could organize a team lunch this Friday! How would you guys like to go out to "x"?
Going out to lunch and possibly grabbing a drink together is probably the best way to socialize, but it will depend on the company whether this will actually happen or not. If having a drink during lunch if "verboten", then maybe suggest Friday after work instead.
3) Friendly gestures
I would also suggest bringing in some snacks for your team once or twice to "break the ice". Here in Canada I would, for example, recommend getting a box of tim-bits (cheap and yummi, I don't think I know a single person who would refuse one) and offering it to them. You may want to offer something more appropriate to your location - even a cheap box of cookies.
Hey guys, just wanted to come over and say hello. I was in the store this morning getting my coffee, and I thought everyone might like to start their day with a cookie! (hand some out to everyone and invite them to come to your desk to have more if they want!)
4) Keep going
Once you've connected with people and learn a little bit about them it's going to become a lot more acceptable for you to walk over and just chat for a little bit - especially when you know what they like to talk about.
Similarly, you may invite them to drop in every once in a while and "pick your brain", or just have a friendly chat.
Remember that if you sit in your corner and don't make a move you are sending a message that you are anti-social. If they are equally shy in approaching you then you need to take these steps pronto.
Please note that in a way I blame your team-leader for this situation. He is the one that should be facilitating your integration into the team, not pushing you to take these steps yourself (although they are certainly not a bad idea).