Looks like Veronica or common name speedwell

the flower spikes look very much like Lythrum salicaria. It does develop pretty woody stems and could have started as a volunteer in that Begonia bed.

Here is a link that might be useful: purple loosestrife

Here is a more close up picture. There are quite a few of these plants throughout the landscaping so I don't think they just appeared on their own. They are about 3 feet tall.

Loosestrife?

Definitely Purple Loosestrife (Lythrum salicaria). Beautiful =)

And treacherous. Purple loosestrife is on the Ohio noxious weed list and it isn't legal to sell the fertile varieties. Nurseries in Ohio continue to sell the infertile ones, unfortunately. I say that because they are simply 'self sterile' and will cross pollinate with the fertile ones. One fertile plant can literally produce over a million seeds. It's chokes the life out of wetlands when it gets established there. I read on the Ohio Valley forum that the State of Ohio planted hundreds of them along rte 315 near Columbus. I don't usually go rabid on forums about people's choice for plant material, figuring it's their own call and if they wish to deal with the consequences of their choices on their own property, it's their own business, but purple loosestrife in any incarnation is gonna come and bite this state in the butt eventually.

For what it's worth -- I wholeheartedly agree with calliope!

This is a terrible invasive species in wetland ecosystem, it's choked out all other plants on some parts of the bank of a small creek by my house and nearby marshes, it's even choked out the native cattails, a plant that itself is notoriously weedy.