iSavvix - free service, java-based, compressed disk space up to 10MB (equals 50+ MB uncompressed). Downloadable commercial version also available.
VMN Storage - 1 GB free storage of music files up to 240 songs, photos and videos. Upgrade to 15 GB storage and more digital files for $9.95 per month or $95.52 per year at 20% savings. Read more about the features here.
Yahoo Briefcase - 30MB storage free; upgrade to additional 50 or 100MB. Public file sharing not allowed under free accounts anymore, but is allowed for upgraded accounts. Upgrades start at $2.95/month or $24.95/year for additional 50MB. Note: upgrade another 50MB to get 80MB total at that price. Upgrades are add-ons at this host and include increase in allowed file sizes, too.

Pay Remote File Storage Hosts

File Genie - subscription service with various levels of storage space starting at $2.99/month for 50MB storage and 500MB/month weblinking (downloading). See explanation here.
Files Anywhere - 50MB free 30 days trial space; upgrade up to 2 GB. After trial period, pay from $3.95/month up depending on plan chosen.
FloppyCenter - 100MB storage at $4.99/month. Free 7-day trial period.
iBackup - subscription, 50MB to 100GB file storage and backup space. Prices from $3/month or $30/year for 50MB.
Streamload - free trial, subscription, unlimited space, note download file size and max monthly downloads limits. Seems mostly for streaming media, but other file types allowed. Upgrades start at $4.95/month for anticipated downloads of 1GB/month. Pay longer terms and monthly rates go down.
XDrive Plus - Subscription, read the FAQs. Plans start at $4.95/month for 75MB and go up to $49.95/month for 1GB. Credit card only.