If you just want to collect the data and not do much with it, then the basic VMware syslog that comes on the vCenter installation ISO works just fine. If you want to take it to the next level and proactively use this data then I would go for a product like splunk or better yet, VMware LogInsight (a bit pricey like all solutions but worth every penny IMO).
Running out of space won't be an issue on the LogInsight appliance. If expansion is needed, you can easily just add another vmdk to the virtual appliance and reboot it. It will then do all the LVM work to increase the disk size for you. You can also archive aging logs automatically to NFS for example.
To start using LogInsight just deploy the virtual appliance and add your vCenter. Next configure your ESXi hosts to use the appliance for their syslog. This can be done via the vSphere client, using a tool provided by LogInsight, or the most fun and satisfying of course is using a PowerCLI command like this.
PS - The following is a pretty good pdf about sizing syslog solutions in general. Although this is from a company that sells syslog products, they did a great job of being vendor agnostic.
http://content.solarwinds.com/creative/pdf/Whitepapers/estimating_log_generation_white_paper.pdf