How much is slower GCM AES-128 than one of the stream chipher eSTREAM? Evaluate the speed of the algorithm GCM AES-128 and compare it whith speed of one of the stream chipher in eSTREAM. Can someone give such an assessment?
eBACS, as given by CodesInChaos, is a great resource, and it provides much more data than I could hope to give in this answer. However, the page is not explicit about whether or not AES-NI was used &mdash; looking at the results, it doesn't seem so.

For an extremely shallow analysis, but allowing us to know for-sure about hardware acceleration, we can use the command-line tool gnutls-cli, which uses GnuTLS to benchmark some ciphers. Some sample output:

[reid@reid-pc] ~ % gnutls-cli --benchmark-ciphers
Checking ciphers, payload size: 16384
     SALSA20-256-SHA1 0.30 GB/sec
     AES-128-CBC-SHA1 0.33 GB/sec
     AES-128-CBC-SHA256 0.21 GB/sec
     AES-128-GCM 1.34 GB/sec
            SHA1 0.56 GB/sec
          SHA256 0.29 GB/sec
          SHA512 0.44 GB/sec
        3DES-CBC 26.96 MB/sec
     AES-128-CBC 0.75 GB/sec
     ARCFOUR-128 0.51 GB/sec
     SALSA20-256 0.64 GB/sec


So, on my system (which has an Intel i5 Ivy Bridge and thus the AES-NI instruction set), AES-GCM processes data at about 1.34 GB/sec while Salsa20-256 with HMAC-SHA1 only manages 0.30 GB/sec.

However, it's thanks to the aforementioned AES-NI instruction set that AES-GCM fares so well. gnutls-cli has another argument to turn off hardware acceleration: 

[reid@reid-pc] ~ % gnutls-cli --benchmark-soft-ciphers
Checking ciphers, payload size: 16384
     SALSA20-256-SHA1 0.30 GB/sec
     AES-128-CBC-SHA1 175.29 MB/sec
     AES-128-CBC-SHA256 136.43 MB/sec
     AES-128-GCM 169.09 MB/sec
            SHA1 0.57 GB/sec
          SHA256 0.29 GB/sec
          SHA512 0.44 GB/sec
        3DES-CBC 26.97 MB/sec
     AES-128-CBC 0.25 GB/sec
     ARCFOUR-128 0.51 GB/sec
     SALSA20-256 0.64 GB/sec


Note here that Salsa20-256 with HMAC-SHA1 outperforms AES-GCM. So, if your requirements allow you to use the AES-NI instruction set (e.g. the near-latest Intel chips), then AES-GCM is definitely the way to go. On the other hand, if your specs are more modest, you may want Salsa20-256 with HMAC-SHA1.

Another benchmarking tool is openssl speed, but it doesn't support Salsa20. Running a benchmark on AES-GCM with openssl speed -evp aes-128-gcm, I get about 1.33 GB/sec, similar to GnuTLS.