How unsafe is it to leave an expensive laptop at a rented apartment or a cheap hotel room? Which precautions should I take?

If you are really only worried about the hardware cost, possibly the safest approach would be to insure your laptop, if you can find an affordable policy. In my case I there was an option to add it to my home insurance. Then the insurance will have a lot of annoying small print about what is excluded, which you need to read. Usually items left in a hotel are covered only if they are in a safe. In mid-range, and certainly expensive hotels there is a safe in every room, but even in the cheapest ones often there is a “safe” at the reception. Then even if it actually gets stolen, you will recover the cost. (disclaimer: I didn’t have to test it in practise)

As a side note, I always wonder if it is better to hide your laptop, or to attach it to something (which will most probably make it visible to the cleaners, etc).

Also, I should note that it’s not the data, it’s the hardware cost I’m worried about (nothing spectacular, about $2000, but still)

Are there any other ways to keep my laptop safe at home besides Kensington lock?

To mitigate the hardware cost in case of theft, ensure that you’re traveling with property insurance. Homeowner’s or renter’s insurance will normally cover your property even when traveling. Computers and other high-value items (e.g., jewelry) sometimes need a special rider on a policy, so you should check with your insurance agent prior to a trip.

I have traveled internationally with PacSafe bag locks for my travel backpack — I would put the laptop in the backpack and then the backpack in the bag lock, and then lock it to a sturdy part of hostels or hotel rooms. PacSafe also has a "portable safe". Both of these items would suffer from a similar bolt-cutter fault, but it is a deterrent nonetheless.

You could rig up a cheap wireless security camera and place it somewhere that the the would-be burglar will see it, like right next to your laptop. Maybe even add a sign that says, “Jesus is watching you.” Something like this camera might do nicely. I don’t know how much space you have in your bags, but if you could stand traveling with it, this would be a workable solution for a hotel or apartment. I guess I’m not sure whether Odessa-dwellers would be deterred by that or not.

Another solution for a hotel, where you can’t fully control access to the room, could be to add an additional lock to the door. Something like this lockS, maybe? It’s possible that will just draw attention to you. It’s also possible that one kick would dislodge the lock. …Well, it’s an option anyway.

If there is a fixed object in the room, I like the Kensington Lock idea, but a table probably isn’t going to do it. With a really short cable, maybe you could hitch it to a large weight set. (Perfect for travel, right?)

@ThornstonS’s idea of leaving cash on a table is a good one. Hide the laptop; leave the cash in the open. I’m guessing most people would take the cash and run. If you don’t want to lose the cash, either, I recommend substituting the cash for a sandwich.

For hotel rooms there is an easy solution: It is called the “hotel safe”. Earnestly, do not store important valuables in hotel rooms. Even cheap hotels have very likely a cupboard which is under constant supervision at least at daytime.

If you have a rented apartment you have another situation. Burglars and thieves have the following mindset: Break in as fast as possible, loot until enough valuables have been found and then leave as fast as possible.

That means for you:

• Fortify your apartment as much as possible on the outside (close windows, lock door even for small distances), but leave everything open inside. Once a thief is inside, he will break everything open if it is locked and easily breakable, causing further damage.

• Kensington locks are only effective against amateurs which have no bolt-cutters
  as vartec already pointed out.
  But still it may work because if he has no cutter it may be too time-intensive
  to break it without too much damage.

• Because the thief is looking for valuables, I hide valuables out of sight
  (The best place is according to my neighbor who is policeman under the kitchen
  sink, the worst place is the refrigerator, the toilet and food cartons because
  these are common junkie hiding places !)
  and normally leave a decoy (some money on the table which looks like change)
  in plain sight. Once he/she grabs it, he/she must decide to go on and risk to
  be caught or search for other valuables which may be non-existent.

One of the most effective measures I use frequently when travelling is Kensington lock. It’s very likely your laptop already has the appropriate slot, so you need to buy the chain and that’s about it. I lock my laptop at any rented place I stay, even if it’s a reputable hotel — no need to take any chances. The cable should fit easily in your hand baggage.

This should be enough deterrent to casual thieves, it’s very hard to take it out if unprepared, and that will surely damage the equipment, which is not what the potential thieves would be after. In your case, when the equipment itself is the only valuable thing, Kensington lock should be sufficient and fairly inexpensive solution.