Does anything actually exist?

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Well, d'you want the explanation of why you can prove your own mind exists?

Basically:
If you do not exist, then there must be somebody or something deceiving you into thinking you exist.
However, to be deceived requires the existence of your mind.
Therefore, your mind must exist.

And yes, you do have to accept the existence of the universe to have any kind of meaningful existence--unless your search is for meaninglessness itself (which is a self-contradiction because meaninglessness has meaning... something, nothing, and the void, remember)...

Anyway, to meaningfully interact with the world, you have to accept three things:
1. The rules of logic are valid. (That is, you have to accept the very basic axioms on faith--things like, "A meaningful statement cannot be simultaneously true and false.")
2. The world outside your own mind exists.
3. Other people you communicate with also exist, and experience the same external reality as you.

I used to ponder this frequently, and i used to openly joke that other countries did not exist...because I had never been to them...all of reality is some sort of elaborate hoax...

Actually, you've got it; the self-contradictory statement that follows from assuming you don't exist is the proof that you do exist. Either you do exist or you don't exist; take "I don't exist" as a statement and follow it to its natural conclusion, and you get a critical logic failure.

If you do not exist, then your existence is a deception.
If it is a deception, then someone has to exist to be deceived.
So, if your existence is a deception, you must exist.

The illogical statement is,"If you do not exist, then you must exist." If a statement leads naturally to illogical conclusions, then the statement cannot be true.

"Is it true that everything is an illusion, and nothing exists? In that case, I definitely paid too much for my carpet."

- Woody Allen, in The Thing With Feathers

(which also includes the title quote: "Emily Dickinson was wrong. Hope is not the thing with feathers. The thing with feathers is my nephew. I must take him to a specialist in Zurich.")

Nothing exists. That's why I stopped worrying about anything.

Seriously though, have a look at G. E. Moore's article "Proof of an External World" (see this link). It's interesting reading.

I have been pondering the nature of existence and I have pondered the idea of non-existence being a category of existence. I was toying with existence having multiple dimensions, rather than the simple dichotomy most reduce it to "either something exists or it doesn't". How about something can "kind of" exist? Take the idea of the "three-sided square" for example. Most would say that it can't exist because a square by definition can only have four sides. But if it doesn't exist, then why does it exist as a concept capable of analysis? A three-sided square does exist, but not materially.
Then I pondered the idea of the supernatural. I evaluated this as an agnostic and an atheist. I realized that objects can exist conceptually and materially, so overlap is possible. However, there is no evidence of the supernatural interacting with the natural. Through science, a plethora of natural events can be explained under natural laws and there is little reason to believe currently that events with no explanation can't be explained later. i decided then that supernatural, in the religious sense, would be the wrong term to use. Rather, I decided to use it in the more etymologically correct sense, as a realm out of the perception of those belonging to the natural realm. It can not, by definition interact with natural existence.
Separate from the supernatural category, but capable of overlapping with it belongs concepts we can not conceive of. This one is kind of similar to the supernatural in that natural beings can not experience them. However, the supernatural focuses more on things related to what we consider objects while the other focuses moreso on things related to concepts. Since for us, concepts and objects can overlap, but are not necessarily synonymous, likewise, those two categories interlap but are not synonymous.
Things which we consider to not exist, actually exist conceptually. Things which "don't exist" because we can not experience them due to our natural existence, belong to the "extranatural". Hope I made sense
*Perhaps extranatural may be a better term than supernatural as it more readily conveys the sense of existing =outside= rather than a hierarchal existence.*

To paraphrase Ayn (hopefully not too badly) "the world exists, it is how it appears, deal with it as such; you have senses, use them, work out what the result means; attempting to place your own fancies before reality will ultimately lead to your disillusionment and downfall; the world doesn't care what you think about it, it just is."

nop, were all part of a big matrix thing?