Many threads on here are negative or complaints, so here's a positive one.
I decided to get an S4 on Telecom, as 2degrees coverage wasn't good where I want to use my phone, and they won't roam to Vodafone in areas they think they cover. I went into a store, there was a ten minute wait for a staff member, but once I saw someone it took 30 minutes to get the S4, transfer my number, and put the phone on credit (hey it was interest free, why not!).
The number ported to Telecom in about four hours. I was initially a bit confused about how to set things up like voicemail, but after calling Telecom they told me about the booklet in with the SIM card, as well as telling me what I wanted to know. Their helpdesk answers calls reasonably quickly. The phone works really well. The network coverage is really good. Data speed is really good in central Wellington. They even called me to follow up to make sure I understood my plan, my phone, and offer a free lesson. Paying my first bill by credit card took a bit of time because of their slightly inflexible phone tree - I hit the wrong button once and would've had to hang up and start again so instead I hit 0 to talk to a person - but once direct debit kicks in no problem.
So far Telecom is doing everything right. Fingers crossed things continue on this way :)