Which items to buy at All Random Deathmatch?

I try to stick to very neutral items at first, and if I feel like I'm going to have a good game I'll start building more role specific items.

Boots

I will always get either Power Treads or Tranquils. Power treads are nice because they provide stats for every role. Tranquils are nice because they allow you to roam easier and keep you in lane longer. Both of these benefit almost every hero in the game a good deal. The other three boots are a lot more situational so I tend to avoid them, unless I'm rocking it as a hero who generally needs Boots of Travel.

Core

There are a handful of items I will get every game, and then some I'll get depending on my mood. For every game I like to get:

• Aghanim's Scepter - This items has the stats, HP, and Mana that every hero can benefit greatly from. There are a ton of ultimates in the game that are improved by this item, and it seems every major patch Icefrog is adding more ultimates to that list. You really cannot go wrong with grabbing this. It's generally the item I build right after my boots, even if I don't currently have a hero that has an ultimate that applies.
• Blink Dagger - Every game. Every hero can benefit from. I don't care if your hero already has amazing escape, get this. It gives you just one more, which will keep you alive longer and gives you the ability to get the jump on the enemy team.
• Black King Bar - This item will make sure you can go into fights and not be disabled the entire time. BKB ensures that you actually remain useful during engagements, and greatly aids in your survivability. Plus it gives you a little bit of strength (health) and damage.
• Orchid Malevolence - This is generally my last item. It gives a lot of intelligence, attack speed, damage, and mana regen. Attack speed and damage benefits everybody, intelligence and mana regen benefit most everybody to a lesser extent. The active is what we want here though: A 5 second silence + damage amplification! That 5 second silence is an eternity in Dota. With it you can just entirely shut down their support or any big ult they have. A well timed and placed Orchid can win fights.

Situational

These are items I get really depending on my mood. It's hard to have situational builds in ARDM since the situation is constantly changing.

• Sange and Yasha - I get this probably half the time. It has pretty nice stats, good movement speed increase, and the maim is useful for ensuring heroes don't get away from your team.
• Mekansm - I just realized how weird this item is spelt. Anyways, this item benefits your whole team! If I'm feeling supporty and nobody else is building one, I'll grab this pretty early on. This once lead to humorous game where I randomed Riki first, expected to die soon so I start going a support build. Ended up never dying, had Tranquil boots, Mekansm, Aghanim's, and BKB. Was a weird build, but hey it worked.
• Pipe of Insight - This is a pretty good item. Lets your team block a good bit of magic damage (400 I think). If they keep getting big spell casters then pick this up to keep your team alive through the nukes.
• Urn of Shadows - This item is incredibly cheap and incredibly useful. If I'm feeling supporty and someone else grabbed Mekansm, then I'll grab this. Or I'll grab both! Having a Mekansm and Urn of Shadows on your team means nobody ever has to go back to the fountain. You are a mobile fountain! The DoT also helps make sure nobody gets away with 17 HP.
• Force Staff - Another incredible utility item. Need an escape? Force staff! Need to chase down someone? Force staff! Want to surprise that annoying Drow hiding behind their tower shooting you? Force staff her into your face! Such a great and fun item it's hard to ever pass this up. This item is so good it might need to be a core item.
• Shadow Blade - This is an item I like to get very occasionally. There are a good number of heroes that this item is basically on a must on, and every hero barring Riki and Clinkz benefit a little bit from this. It helps initiate fights, helps you escape, helps you gank, and you even get a good bit of damage from it. And if you happen to random a Witch Doctor in the game and you have your Shadow Blade, oh man. Not much is scarier than an invisible Witch Doctor Aghanim ultting your team.

Of course depending on how "situational" we want to get, this list could go on for a very long time. But these are probably my top situational items I get in ARDM.

Misc.

These are items I didn't mention above because they're just so cheap, but you should be aware of them.

• Magic Wand - This items is so awesome. Every single hero in the game benefits from this. It is super cheap (500 gold I think), and provides free heals and mana all game!
• Observer Wards - Someone has to buy these. In ARDM, everyone should be playing a little bit of support. This means occasionally you'll need to buy wards. Don't ever let the shop have 2 stacks, and if you look and there are 2 stacks sitting there, buy a set! I don't care if you're a 7 slotted Void, buy the wards.
• Sentry Wards - You should be dewarding, but I know in pubs that doesn't happen very much. If you're feeling good and you're pretty sure they're warding you, then buy these. Or if they just have a stealth hero obviously grab these.
• Gem - This is item relatively cheap at 900 gold, but lets you deward everywhere you go. Also puts an end to any stealthing the enemy team wants to do (and if they read my guide, then they will all have Shadow Blades!).

These are just the items I tend to look at in ARDM. The other suggestions are also great and could supplement this list. Utility items are always a good pick in ARDM as they benefit everybody. The only real utility item I do not recommend is Linkens Sphere, as WizLiz has covered in their post. Even the utility is amazing, it is just too situational.

There are some items that are reasonably general purpose, regardless of what hero they are on (stats are always nice). Drum of Endurance is probably the most obvious example. Some others that have some versatility...

• Orchid Malevolence
• Vladmir's Offering
• Heaven's Halberd
• Necronomicon
• Mekansm (assuming no one else on the team gets one)
• Medallion of Courage
• Pipe of Insight
• Linken's Sphere
• Black King Bar
• Eye of Skadi
• Scythe of Vyse

Some other items might be a bit less general purpose but usually are still a safe bet to offer a benefit...

• Blink Dagger (useless on a select few heroes that already have a blink or blink-like skill, but usually a good choice)
• Assault Cuirass (less valuable on non-right-clickers, but you'll still benefit the team)
• Desolator (Ditto Assault Cuirass, but with the added danger that the effect is nullified on heroes with a natural Orb effect like Antimage or Viper)
• Shiva's Guard
• Manta Style (Far better on Agi heros, but there are enough stats for others too, and the active cancels Silences)
• Force Staff

And or course, wards are always good!