would this trash the ice in the server? 

Assets, Upgrades, and Agendas (and things hosted on them, if any) are "in" a server.

Ice installed above them are "protecting" the server.

This is a key distinction in the game, and many cards hinge on this fine point.

So, this card...

When it came out I shrugged and put it in the box. Too expensive, too slow. If you are paying $4 and an extra click to play the card you could probably afford to trash whatever is in the server and access it as well.

However, I've been starting to play this card lately and it's been doing some work for me.

The increase in usage of upgrades such as Ash, Caprise, etc and what seems like an uptick in usage of Cerebral Overwriter and various Mushin No Shin shenanigans has made it sometimes useful to run over and frag a remote with two or more cards installed in it without accessing them.

Also, Prepaid Voicepad. I swapped in a 1-of into a PPVP Express deck and it has been surprisingly effective in that engine. I've even Same Old Thing'd this card before which was painful but took out a super server with a couple of upgrades and what turned out to be a Reversed Accounts. Situational for sure, but it definitely made a difference. Also, in addition to the PPVP discount, Express effectively pays one less for the card and Desperado procs for a buck as well, so it's very economical for him.

I've also had good use of 2x in Quetzal, though in that deck it's more of an early pressure gambit.

Anyway, long story short, I like Singularity as one of many examples of a card that was underwhelming when released, but starts to look more viable as the card pool grows and the meta shifts. That's probably my favorite part of netrunner; the fluidity of it feels (to me) greater than that of MtG and other CCG / LCG games I've played.

Note that this is a beatuiful combo with Eater, which allows you to make inexpensive runs on those remotes and wipe out the server without accessing.  It can be absolutely brutal, especially in an eater-reliant deck.

Note that this is a beatuiful combo with Eater, which allows you to make inexpensive runs on those remotes and wipe out the server without accessing.  It can be absolutely brutal, especially in an eater-reliant deck.

Yup. Does not, however, combo well with Blackmail which I figured out only during the middle of my first game with my Valencia Eater deck. In such a deck I do NOT want to give the Corp any opportunity to rez ice on their remotes if it can be avoided, and of course making a Singularity run is counter to that general strategy.

Seems obvious in hindsight, but we all have our "der..." moments I suppose. Suffice it to say, Singularity was removed immediately afterwards.

I've had some success in my Valencia take - I usually use it as my escape valve on the 'I have no choice' runs that come mid-to-late game.  Basically, if I can't be sure what that card is, I can singularity in and remove it.

Useful, sure.

However, I think you're ultimately very right, as it makes that server ONLY vulnerable to Singularity, and ... well.  Just no.  It's being replaced for three Infiltrates instead, I think, as the point of the thing becomes to know when using that blackmail is worthwhile, and when it isn't.  

Yep, I'm running Infiltrate in my Valencia deck in fact. I'd prefer the Criminal version that exposes 2 cards...Satellite Uplink , but can't spare the influence.

dimithrone, the runner trashes them so they go in face down. 

I play Industrial Genomics, so I have to know this, but it's amazing how many Runners do not.

Page 5 of the FAQ:

The Runner never accessed the card(s), so there's no reason for him or her to have seen it/them. The Runner is inferring a magical effect to Singularity that it doesn't have: it doesn't say "reveal" or "expose" before trashing. If the Runner is trashing facedown cards with Singularity, he or she has no direct way of knowing what those cards are.

Page 2 of the FAQ discusses Archives, mentioning that: