I'd go with Dana-Tenacitys advice - once you've got it clean.
IMHO keeping it natural and not using using any form of oil looks the business. It is what all the huge teak decked mega yachts do, and what's good enough for them, should be good enough for us mere mortals........
If the deck you have is dirty getting it clean does take some work - but if you always remember teak is relatively soft so you should avoid any form of pressure, even from a hose, or a brush, if you want to preserve the soft tissue twix the wood grains.
Even rain can damamge teak if it comes down in volume.
Even a soft brush is risk, although we've found it's usually a neccessity when cleaning
off lots of gunk or you'll be at it for days.
We one purchased a 6 year old Grand Soliel which had been left unattended for maybe 3 seasons in the northern hemisphere - and the decks (along with lots more) were positively green with growth. Where the deck was not green - it was BLACK.
We got it back to new by using first a proprietory cleaning
fluid (suspect similar products can be sourced in US but ours was made in UK by a firm called Wessex Chemicals). Our product was diluted and the liquid applied by using a window wiper to spread it evenly over over an already wet deck. Once left for 5 minutes, then with gentle agitation with a cloth or a VERY soft brush (and NEVER with the grain), it brought off most of the gunge. You could actually see the dirt balling onto the surface ready to be flushed away.
We had to be gentle as our product did appear to open the pores (to allow this dirt to lift
out) and one does not want to brush away soft teak tissue with the bad stuff.
So gentle water flow (remember even a regular water hose pressure is TOO much) saw the dirt flushed away, and a second treatment was applied to remove any gunge missed first time round, leaving us with a clean - but still grey deck.
So then on the still damp surface, we chose to use a teak brightener to bleach the dark grey teak back towards a light silvery brown - and thereafter apart for when cleaning up after silly dirt footfalls (usually by visitng engineers) or spillage (oops - too much red wine my dear) - we relied on salt water only.
And even then - did not use a brush - but rather a mop.
Appreciate this level of care may not suit everyone as it does take time - but for me, I still find cleaning a teak deck
is as theraputic as cleaning a swimming pool use to be.
Just shows what a sad git I am, eh?