Is it possible to decrypt an RSA ciphertext with only $N$ and $e$? Is it possible to perform RSA decryption if one only knows $N$ and $e$?

Failing that, what is the maximum key length where brute-force is still practically feasible?
The current best way of decryption an RSA ciphertext (assuming good padding was used) is to factor $N$ into its prime factors $p$ and $q$, and from that, reconstruct the decryption exponent $d = e^{-1} \bmod lcm( p-1, q-1 )$

The current record for factoring an RSA-type modulus (with large prime factors, and not of a special form) is 768 bits.

It is likely that, in the next couple years, slightly larger modulii will be factored; the record for "largest general number factored" has been slowly increasing; someone might manage to factor a 1024 bit number within the next decade.  There is little reason to expect that RSA modulii significantly larger  will be vulnerable to factoring in the near future.