I've had some interesting exchanges with people who've been sending me connect requests of-late. My usual approach - that I will connect with people 'with whom I have done business, or who I know personally' - tends to result in me fending off unsolicited connection requests from a swathe of people who fit into neither category. Of those, one can usually classify the request as being:

• A recruiter, looking to recruit me for a role
• A recruiter, looking for a role for a candidate already on the books
• A recruiter, looking to expand their network in order to potentially action either of the above at some point in the future
• A jobseeker, looking to make connections in order to find a role for themselves - and these are often offshore candidates (plenty from India, Pakistan, Bangledesh, Sri Lanka and South East Asia in general)
• A Sales Manager, Account Manager or Business Development Manager looking to draw attention to their latest innovation that they really want to sell you
• One of the aforementioned three ultimately trying for the same outcome, but being more subtle about it (playing the long game).
• Someone else from the Industry, engaging their LION (Linked-In Open Networker) - basically expanding their professional network for as-yet-unqualified reasons (but in my experience many LION types are also sales-and-marketing focused at some level.)

All of the above - except perhaps the job-seeker and maybe the LION type - are looking to ultimately make money from me. Thus all of them are, fundamentally, sales or revenue-driven networkers who are playing off the numbers - if even 1% of connections over the course of a day/month/year engage with me for business, it's worth the relatively small mechanical effort to click 'connect'.
Many of the above will do little more than that - accepting the 'I'd like to add you to my professional network on LinkedIn' default text that gets shipped with an otherwise ordinary connection request.

As a rule I will ignore the obviously spammy connection-attempts - the ones who are clicking like mad in the hope that one day they'll get a commission derived ultimately from having made contact with me. But many more, i'll flick back a message. "Hi, how have we met or done business before?" And this is where the fun begins... I am variously a) ignored, b) replied to with 'oh, sorry, I must have accidentally clicked connect on you, nevermind!' or c) offered an invitation to connect in order to allow the person to [show me their wares|get me on the roster for future job opportunities|get me to consider their professional services].

One recent conversation - the connection request was from another New Zealander, and someone working as a BDM for an organisation with whom I have a history, albeit not in my current role - referred me to https://www.linkedin.com/pulse/linkedin-ruin-steve-houck as part of a wider discussion of 'What is LinkedIn for?' And there are aspects of the content of that article that I very much agree with.
So when should you connect with people on LinkedIn?
My thoughts at this stage - and this post is largely off the cuff - are:

• LinkedIn is used in the western hemisphere as a 'professional networking' tool - not just recruitment, but also a way to make-and-retain connections with people you do business with. Buy, Sell or Partner. Vendor-Customer, Supplier-Wholesaler, Engineer-Engineer.
• If the invite is coming from someone that you think you might actually get value from, by all means accept it! But think about it. What is their interest in you? Is it to keep-in-touch? Or are they fundamentally hoping to simply see you as a dollar-sign?
• Absolutely use LinkedIn to connect with people that you've worked with before; that you've done business before; that you know from circles outside of your work if you have the kind of relationship that supports it. I regularly search LinkedIn when establishing contact with new potential suppliers or customers, just to see what I can find out. That little bit of extra perspective can be key, especially if you have friends or networks in common.
• If you're job hunting, keep your LinkedIn up-to-date and ensure your privacy settings are appropriate. You want to sell yourself, that's cool. My experience - as a New Zealand based IT manager - is that candidates who've put some time into their profile and represented their skills and experience well, do better - and this despite the typical NZ IT market scenario, where pretty much any job will come via Seek, TradeMe or a recruiter engaged for the purpose.
• If you are in a Sales or Marketing role, build a relationship with the person with whom you wish to connect. Find a way to meet them IRL, or send a personalised introduction. Leverage shared networks, contacts or connections. Don't emphasise your desire to sell something. Emphasise instead the value you bring. And expect to be evaluated harshly by receivers like myself, who are dubious of 'spam' in the form of a LinkedIn connect request.