I’d still like to avoid using anything web-based.
Think they’re pretty much all web-based nowadays. However a lot of programs will let you export GPX files, meaning you can use whatever software you happen to have to analyse them.
The only real advantage of non web based things is that you can use them whilst you’re off the net if you take a laptop out places with you. Whilst online things might not be 100% secure, you surely trust the internet with far far more important data than how many bike rides you’ve been on – your email account for example. Something like endomondo with all the privacy settings on will be just as secure as (say) email – ie. you’re completely at the mercy of whoever operates the server as to whether it is secure, but it is very unlikely that anyone else will get your data.
After all, you are using the gps tracking software on a device that is constantly connected to the internet, you only have the word of the software maker that it isn’t uploading your every move to the whole world anyway.