Publicly available genome sequence database for viruses? As a small introductory project, I want to compare genome sequences of  different strains of influenza virus.
What are the publicly available databases of influenza virus gene/genome sequences?
There area few different influenza virus database resources:


The Influenza Research Database (IRD) (a.k.a FluDB - based upon URL)


A NIAID Bioinformatics Resource Center or BRC which highly curates the data brought in and integrates it with numerous other relevant data types

The NCBI Influenza Virus Resource


A sub-project of the NCBI with data curated over and above the GenBank data that is part of the NCBI

The GISAID EpiFlu Database


A database of sequences from the Global Initiative on Sharing All Influenza Data. Has unique data from many countries but requires user agree to a data sharing policy.

The OpenFluDB


Former GISAID database that contains some sequence data that GenBank does not have.



For those who also may be interested in other virus databases, there are:


Virus Pathogen Resource (VIPR)


A companion portal to the IRD, which hosts curated and integrated data for most other NIAID A-C virus pathogens including (but not limited to) Ebola, Zika, Dengue, Enterovirus, and Hepatitis C

LANL HIV database


Los Alamos National Laboratory HIV database with HIV data and many useful tools for all virus bioinformatics

PaVE: Papilloma virus genome database (from quintik comment)


NIAID developed and maintained Papilloma virus bioinformatics portal



Disclaimer: I used to work for the IRD / VIPR and currently work for NIAID.